| |
Years of
technical only explanations in trying to teach computer aided design
(CADesign) have been found by this author to be not very effective
resulting in digital future shock. Most digital based design
applications in the last twenty years have not reached beyond the
dimensional boundaries of paper based processes and their attending
cultures and social structures. Thus, this chapter takes a unique
approach by presenting a digital way of thinking and techniques for the
digital based three dimensional computer aided design process. So, we
will begin with an introduction to the digital way that includes
digital ethics, responsibilities, 3D dimensional orientation and
description of the differences between paper and digital design
processes.
The most
difficult, expensive, time consuming to develop, and important part of
all digital systems is the human part of the system. The human part of
most digital systems is usually defective or broken. Because of the
lack of understanding of digital technologies, most digital systems are
applied in the same way as the past information technologies they
replace. The result is the growth of digital systems being blocked by
technically obsolete constructs and old social structures of the past
paper, radio and video based analogue information systems. The human
part of current digital systems has yet to make the transition to
digital based, interactive networked information systems. An example of
the inappropriate application of current paper social structures to
digital are the present copyright and patent laws. Because of the
nature of digital data, these are difficult or impossible to
enforce with regard to digital. Digital data is physically easy to copy
and modify. Ownership of digital data can not be rigorously proved.
Digital data costs almost nothing to copy. If you share digital data
with a friend, you still have it, unlike an apple or loaf of bread.
Your friend can easily add to the data and modify the shared data.
Because of the dependencies in the complex world of digital data, the
natural tendency is to share data or be excluded from evolving systems.
The more you share digital data, the more there is. The more there is,
the more it is used and the more digital technology grows. An example
of this phenomenon is the great digital growth in the United States
(US) in the 1980s. In 1981, IBM introduced its personal computer (PC)
for use in the home, office and schools. Due to the open architecture
of the IBM PC, the 1980's saw an expansion in computer use as clones of
the IBM PC made the personal computer even more affordable. The number
of personal computers in use more than doubled from 2 million in 1981
to 5.5 million in 1982. Ten years later, 65 million PCs were being
used. The growth happened because of the freedom to share and modify
digital data, processes and technical information. All of the technical
information for the hardware and the source code for software was free
and open. It is a very simple idea -- if digital technology is open,
can be freely used, modified, and shared by everyone, then digital
technology will grow very quickly. This digital reality is in conflict
with traditional social structures that currently close digital
technology by high costs through copyrights, patent laws, and other
forms of traditional ownership.
| 0.2
Common
Good
Public
License |
Digital
technologies and its effect on humans and their social structures
should be of the greatest value and interest to the scientist and
academic person, but receives little or no attention in comparison to
technical issues. Because digital technologies are based on global
sharing of digital information, those creating and using new digital
technologies have the obligation to support: digital freedom, human
rights and a sustainable future. Because digital computations of the
personal computer are predicted to equal capabilities of the human
brain in the next twenty years (The Age of Sprirtual Machines,
Ray Kurzweil, Viking/Penguin Group, New York (1999) ISBN 0-670-88217-8)
a deeper commitment to ethics and global openness by the creators and
users of digital technologies is required to secure a safe, stable
future for all. The development of digital technologies under the
Common Good Public License (formerly known as the Greater Good Public
License - in short, CGPL - http://www.ggpl.org)
agreement,
for
example,
and
its
three provisions where all developers
and users agree to use the technology to promote digital freedom, human
rights and a sustainable future, is not only possible but it is the
digital future.
You are free
to use this text and any ideas contained here, if you agree to share
this knowledge freely and use it to promote human rights and a
sustainable future. Please use this text in a special way. The person
reading these words should doubt, question and reflect upon how their
senses, perception and reason may deceive them. The person learning the
digital way needs to learn to think in a very special and systematic
way about computers and other digital devices. The following are the
three steps in learning to think in this special way. You must walk
these steps many time before you will understand the digital way.
- First - define digital.
A person should carefully describe the nature of
digital materials.
- Second - understand digital processes.
A person should try to understand the logic for the
existence of digital
processes stemming from the nature of digital
materials.
- Third - derive first principles of digital.
When a person understands the nature of digital
materials (size, weight,
speed, and cost) and the nature and relationship of
materials to processes,
it is then possible by logical reasoning to reveal the
first principles in the
development and application of digital devices and
understand the
emerging digital culture and social structures that
arise from the use of
digital devices. This special systematic way of
thinking does not rely on
our physical senses, but on complex logic sometimes
called scientific
thought, which requires "rigorous proof" of an idea.
An idea such
as the sun moves around the earth must be proven by rigorous logic, observation and testing not
just by simple observation. An example of how we are deceived is shown
by the fact that we can not feel the movement of the earth. However we
are told that the earth is moving in an orbit around the sun, that the
earth and its orbit around the sun, the sun and the rest of our solar
system are moving at great speeds through space, but we can not feel
the speed at which we are moving or easily see any movement. We see
clearly the sun moving across the sky, and with no other information we
would reason that the sun revolves around the earth, but we are
deceived. Currently we see that a computer screen displays information
that was in the past displayed on a piece of paper, and we would reason
that it is the same as a piece of paper and we can use the computer in
the same way as we use paper, but we are deceived about computers and
what they have to offer. Fully understanding computers and the digital
way and what the future holds requires a person to doubt the current
use of computers and ask:
- What are digital materials?
- What is digital culture?
- What are digital social structures / laws ?
- How long does digital data last?
The
answers are not what you would expect. How much will change in future
years will surprise most everyone and may be difficult to deal with.
If you have any questions, please mailto:carl@applied3d.org
The Computer
Aided Design (CAD) study in this chapter gives an overview of
underlying general principles concerning multi-dimensional modeling
including orientation, operations and applications. This chapter's text
includes the following:
- Discussion
about
digital
materials
and
processes.
- Presentation
of
the
Cartesian
coordinate
system.
- Handedness
and
orientation
in
three
dimensional
space.
- Concepts
of the multidimensional digital design process.
- The
differences between: Visual Representation, Boundary Representation
(B-rep), Constructive Solid Geometry (CSG) Representation, Function
Representation (F-rep)
The first
objective is to provide a digital world view in the discussion and
demonstration of multidimensional modeling which shows the differences
between paper and digital material and processes. The second objective
is to demonstrate basic methods used in multidimensional modeling. The
third objective is the realization that the user interface must be as
simple as possible so as not to interfere with the creative thought
process of the designer. The fourth objective is to outline a set of
basic functions for a 3D CAD modeling system which can be used as a
specification for multidimensional modeling systems of the future.
| 0.7 Paper Design Overview |
The paper
based design process for a new product model takes a long time. It
involves many people typically working in a large hierarchical social
structure divided into three functional design phases: conceptual
design by experts in a research group, working design by an engineering
department, and production design by the manufacturing department.
Paper design involves people with various levels of different skills
and academic degrees such as in physics and mathematics. It also
involves highly skilled drafters needing years of technical training.
Drafting on paper is the principal process. Drafting is
done for the purpose of control and verification that the design will
work . The actual verification of the design is best done by producing
a product prototype. This requires yet a different set of highly
skilled people. When the product is scheduled for production it often
needs modifications so it can be produced effectively.
| 0.8 Digital Design Overview |
Digital design
based synthetic simulation allows levels of interactive design
detailing and verification not available in the physical prototyping
processes. A hierarchical structure involving many highly skilled
people doing many disparate tasks is not necessary. The long time from
conceptual to production designs is drastically reduced from years to
months and from months to days. The process is only hindered by the
ease of navigation in Cartesian space that imposes demands for a highly
interactive and yet simple, intuitive human interface. Digital
designing offers so much more than paper and physical processes, yet
the change over to digital design is very slow because of lack of
understanding and overcoming entrenched paper based hierarchical social
structures of the past millennia. There are still technical issues to
be addressed. However the development and implementation of
multidimensional modeling is more of a social problem than a technical
problem.
Note: At the end of the
chapter there is a list of software resources and exercises. Three
dimensional visual spatial navigation and modeling is understood
through experience and reflection on that experience. It is recommended
that you use the HTML version on the CD with animated GIFs and the free
programs provided.
At each new level of
energy input to a given system, that system may cross boundaries of
discontinuities creating instabilities. The invention of digital
devices and the rate of technological advances stemming from these
devices are creating social discontinuities that often do not allow for
recognition of the capabilities or allow for the full use of such
digital technology in certain sectors. This is especially true in
CAD.
Sometimes inventions do
not flow out of previous inventions. This adds to the confusion in
transitioning to the new technology. The pencil did not evolve into a
computer. While both are tools that serve a common need for human
communication, one did not evolve from the other. A comparison between
pencil and a computer seems to hardly have any relevance because there
is such a great difference. The paper and pencil are very simple
objects and are easy to use for simple communications. Because of these
limitations, drafting, which relies heavily on the use of paper and
pencil is difficult, complex, slow and inaccurate compared to computer
based engineering and design practices. Although computer based design
and engineering has its own complexities that need to be overcome, it
is relatively easy, fast, precise and practically unlimited in nature.
Again a comparison between an imprecise analog line drawn on paper and
a digital model of a line on the windshield of your computer design
system is so great that a comparison should seem to be irrelevant or
even silly. However most people do not make the realization that a line
in the computer is dynamic: able to be copied perfectly, rotated,
shortened, lenghtened, divided, offset, mirrored, arrayed, has no width
yet carries sixteen decimal places of accuracy. In fact, it is
functionally alive; there is no parallel on paper.
The paper drafting
process and procedures based on the simplicity of paper and pencil have
severe dimensional and dynamic limits in comparison to the computer
modeling process. Paper drafting is two dimensional media. It fakes
three dimensions through front/side/top projections or 3/4 views drawn
with illusive isometric perspective, or fake exploded views. The skill
and training requirements needed for designing using drafting
procedures are very high. Six years of math to be an engineer plus two
years of drafting classes equals a total of eight years of training.
The basic tools used in paper drafting procedure are very simple in
comparison to the computer design tools. However in application, the
engineering and design based drafting is far more complex, difficult
and slow to use in comparison to computer based engineering and design.
The paper drafting process is very inaccurate because of the
imprecision of the materials and the need for working to scale, the
computation of that scale and dimensions by hand-held calculator and
the use of complex geometrical projection drafting procedures required
in faking a reality of three dimensions. The computer drafting process
where the computer is used as a simple substitute for paper and pencil
uses the exact same procedures as the paper drafting process and is as
inaccurate and slow if not slower than paper drafting. The users of a
computer paper drafting system will say they are much faster using
paper and pencil in comparison to using a computer. The computer they
say slows them down and is too complex to set up and maintain. They
very often laugh and say that the computer is just a very expensive
electric eraser. They will admit that it is a little faster in the
creation of labels and drawings are cleaner and look better. The fact
is that if they use the computer as a substitute for paper, they are
quite correct in their observations and should limit the use of
computers in their operations and should continue to use their
traditional drafting processes. The typical computer drafting
workstation includes a electronic drawing pad, plotter, a hand-held
calculator, pad of scratch paper, pencils, technical pens, drafting
board and all of the other supporting equipment and tools to do cut and
paste of paper drawings. On the other hand a computer aided design
workstation requires only software, PC, mouse, keyboard and a
plotter when the output is paper drawings.
| 1.3 Paper Computers and
CAD |
A computer is
a very powerful general-purpose tool, that can be used as a simple
substitute for pencil and paper. The Macintosh computers were designed
to be easily used as a substitute for pencil and paper. So of course
the Macintosh by many of its users is seen as a typewriter and used
only as a typewriter for the sole purpose of making paper documents.
Macintosh users typically do not know how to share files or how to use
any of the advanced capabilities of a computer. In the same way, many
current computer aided design systems are actually computer aided
drafting systems. Their user interface has been designed to be similar
to the use of a piece of paper and like the Macintosh applied to
drafting as a simple substitute for paper and pencil using the drafting
processes and procedures that have been developed over the last 400
years. The people who use computers as a substitute for paper and
pencil have no idea how to really use the powerful capabilities offered
by computers.
That the use
of computers as a substitute for paper causes confusion between
drafting and multi-dimensional computer design is reflected in the
understanding of the acronym CAD itself. Many who use the paper
processes for design believe the acronym CAD stands for Computer Aided
Drafting (CAD), but the acronym stands for Computer Aided Design (CAD)
as first claimed by the United States Air Force materiel's lab. The
users of CADrafting do their calculations with a hand-held calculator
and call what they are doing drawings, and these drawings are as full
of mistakes as the paper drawings drawings that preceded them.. In
comparison, the users of CADesign do their calculations using the
computer to create geometric constructions through the view screen into
multidimensional space. The users of CADesign are not drafting and
faking dimensions. They are modelers modeling precise multidimensional,
mathematical models.
| 1.5 The Extinction of
Drafting |
Computer Aided
Design (CADesign) did not evolve from drafting even if both serve as
design tools and the processes are confused by most. Designing with a
computer by creating models in multidimensional space requires very
different procedures, processes and rules than traditional drafting.
The CADesign processes are as different from the drafting processes as
a pencil is from a computer. The CADesign system uses digital media to
create a precise mathematical model in multidimensional space and then
create a flat projection from that model in order to produce an
accurate set of paper drawings with a plotter. Yet many people continue
to use CADrafting which is only a substitute for paper and pencil and
nothing more and reject the computer's capabilities, dismissing the
advantages of multidimensional space as too complicated. However, as
the power of the PC is increasing, CADesign technology is prevailing,
particularly with a new generation of computer users, pointing to the
eventual extinction of CADrafting.
CADesign in
contrast to CADrafting is a multi-dimensional digital media, offering
direct manipulation of 3-dimensional objects. Models can be made
interactive by giving the viewer the ability to fly through buildings
exploring its design, or to zoom inside a machine examining the
relationship of its parts. Models can be animated moving them through a
fourth dimension - time. A designer or engineer using CADesign only
needs to learn a small set of simple rules in comparison to drafting.
Because all mathematical operations can be done visually through
geometric constructions, the designers and engineers do not need the
extensive formal training previously required. A person can become a
master designer or engineer in six months rather than eight years.
Most of the
training given in CADesign is almost always based on learning the user
interface. In reviewing thirty five CAD textbooks on Autodesk's AutoCAD
software application, each text book began by stating that the user
should consider the computer screen to be a piece of paper. None of the
textbooks gave anymore than a history of the development of AutoCAD
commands. None of the textbooks demonstrated how to solve necessary
engineering calculations by doing geometrical constructions. Most of
the textbooks consisted of exercises for each command, but they only
dealt with two dimensional applications. Yet none of the exercises took
into account the rules of drafting and the drafting specifications for
the creation of paper drawings. None of the textbooks offered a
systematic approach to creating models in Cartesian space and then
being able to use the models to create paper drawings.
| 1.8 CADesign, a
Cyberspace Ship |
The computer
screen of a CADesign's workstation is not a piece of paper! It is the
windshield of a cyberspace ship - the face shield of a small personal
virtual jet ski surfing, probing, and exploring the vast virtual
universe. Understanding the true nature of the digital materials and
processes as practiced in CADesign systems is essential to making the
most effective use of these systems. CADesign is not merely a
substitute for drawing on paper. CADesign is a new digital media
device. It is a multidimensional modeling space that allows you to make
simple virtual bit stream - blocks, spheres, nuts, bolts, pistons,
molecules, cells, so on - realities that can evolve into complex
virtual and synthetic life streams - ever more complex assemblages of
data. This digital flux will expand our consciousness and create a
network of synthetic awareness of the world unlike anything we have
ever known.
Only
a few people who are digitally literate have come
to understand and develop an intuition concerning the social impact of
digital materials and processes, but even they most often consider
synthetic worlds to be parallel worlds to the natural world with little
connection between the two. However the practice of CADesign
demonstrates that synthetic worlds are very much a part of the natural
world and the natural world will be greatly affected by synthetic
objects created with these systems. CADesign systems are the critical
link, bridge or transportation device that connects digital realities
to the natural world.
The
new digital structures are creating future shock.
The confusion between CADrafting and CADesign is an example of this
future shock. Legal ownership of digital materials, 0's and 1's, and
their associative digital data, bit streams and processes cannot be
rigorously proven or verified causing misunderstanding as to value. For
example, Netscape, though highly successful, never created a positive
cash flow for its investors. The failed dot coms caused financial
instability of the stock market. Digital bit streams are more illusive
than water or air, where only the ownership of the land through which
they flow can be proven by traditional law. Digital material and its
attending virtues are bringing to question the validity of ownership,
and this suggests that ownership should be replaced with stewardship
and service. The value of digital materials depends upon their use, and
unlike analog materials their uses are unlimited. Unlike the analog
process of copying, where the copy degrades from the original and the
process is thereby limited, the digital process of copying does not
degrade and costs very little in comparison to the analog process. The
extreme difference between the digital and analog processes is
expressed in the basic conflict between the idea of openly sharing
digital information and the concept of proprietary ownership.
Currently, companies use the CADesign process to create proprietary
designs and patents on which they depend to create value on the stock
market. They have no interest in sharing that information with anyone.
Therefore most of the software companies that provide CADesign systems
have no interest in their systems having any compatibility with any
other systems.
| 1.11 Virtual
Networked Organisations |
In the digital world no one has ownership and the idea
of product is being replaced with the idea of service. This is really
not much different than the actuality of business today. Most people
who conduct business do not own patent rights or copyrights but are
simply providing a service. The overwhelming efficiency and convenience
of CADesign will promote the development of direct manufacturing.
Consider the following future scenario. Choose an object that you want
from swarms of cyberbody information. The object will modify itself to
suit your needs and directly manufacture itself. Materials will be
recycled. This will be a reproduction service having little or nothing
to do with ownership of the original design, tooling and or production
facilities. The design and production processes will become self
modifying. How then can one judge who owns a patent or copyright to a
design created by automated processes. Businesses of the future will be
digital structures called Virtual Networked Organisations (VNOs),
organic growth models featuring no central control or job descriptions.
[ For further study on the subject of VNOs, please refer to the paper:
"Management and Virtual Decentralised Networks: The Linux Project" by
George N. Dafermos, First Monday, volume 6, number 11 (November
2001), URL: http://firstmonday.org/issues/issue6_11/dafermos/index.html
]
Because of its
application value to design and drafting, CADesign software
applications continue to be some of the most expensive and profitable
personal computer software in the world. The profit in CADesign
software is second only to operating system software. At the start of
the PC revolution in the United States, AutoCAD software by Autodesk
became the de facto standard for many years in personal computer
computer aided design software and was second to Microsoft in profit
measured in billions of dollars. Profit however is not the reason to
study CADesign. Multidimensional modeling and synthetic simulation are
some of the most challenging and important technologies in the field of
computer software.
| 1.13 Control the Replicators
|
The importance
of computer modeling / CADesign is only understood by a few people who
have been in the field of manufacturing and production involving the
application of numerical control (NC) machines or other digitally
controlled processes. Studies made about the development of flexible
automation show that multidimensional and accurate digital data and
speed of processing is the limiting factor in the design, development,
manufacturing and implementation of a cycle of new devices. The length
of this cycle was critical to the US Air Force who needed a new fighter
plane to fight a jungle war in Vietnam. The lead time was 5 to 7 years
for the development of a fighter. Acquiring the data needed for the NC
equipment and the associated tooling to assemble the fighter were the
bottleneck in development. It is this author's opinion and experience
that the big four companies of the US military industrial complex have
blocked the development of small, just in time manufacturing units and
flexible manufacturing, because this type of development threatens
their combined monopoly on the manufacturing of military equipment. As
the power of personal computers continues to increase, so does the
value of virtual models. Virtual models will quickly be pushed to the
higher level of synthetic models. Automatic digital design agents
capable of design verification and design modification for conservation
of materials will become available. Three dimensional sub micro
printing will create nano machines and thin film flexible digital
devices.
 |
The current
rapid prototype machines using only one type of material will evolve to
use many types of materials, and rapid prototyping will turn into
direct manufacturing. Laser Sintering will be able to create solid 3D
objects, layer by layer, from plastic, metal, or ceramic powders that
are "sintered" or fused using CO2 laser energy. The inherent
versatility of this technology allows a broad range of advanced rapid
prototyping and direct or rapid manufacturing applications to be
addressed. Objects can be designed and made on demand when needed with
this type of replication. Copyright and patent laws from the
centralized point of view block the research and development of this
type of technology. Clearly new social paradigms are needed to allow
and support development of these emerging digital technologies. |
Modeling
systems of the
future will not be used to create paper drawings but the actual objects
of design. The modeling systems will need to be much more accurate than
current systems and to be free for peer review and modification.
| 2.0
Theoretical
Orientation |
Theoretical
orientation includes the history of the Cartesian coordinate system,
the basic theoretical concepts behind the Cartesian modeling system,
and definitions of the Cartesian
coordinate system. Also covered in this section are a digital
learning approach, para-solids modeling kernels, Constructive Solid
Geometry (CSG), and Function Representation (F-rep).
| 2.1 The Cartesian
Coordinate System |
The Cartesian
coordinate system is procedural method used to describe the dimensions
of a synthetic space. The Cartesian coordinate system is attributed
to/documented by Rene Descartes (1596-1650).
Rene Descartes (1596-1650)
|
Descartes is
most famous for having written a relatively short work, Meditationes de
Prima Philosophia (Meditations On First Philosophy), published in 1641,
in which he provides a philosophical groundwork for the development of
the sciences. However, Descartes was a maverick, a freelancer with no
academic or political ties to universities. Descartes radically
asserted all existing knowledge rests on the unstable foundation of
Aristotelian physics based on our senses, perception and reason, which
deceive us. Cartesian physics is a system of synthetic reasoning;
knowledge starts with a first principle and proceeds mathematically
through a series of deductions, reducing physics to mathematics. The
properties of bodies in Cartesian physics are measurable specifically
on ratio scales, and hence are subject to mathematical rendering. The
Cartesian philosophy is the logical referencing of quantitative nodes
of knowledge, establishing these quantitive nodes in a procedural
relationship to create a cellular system of thinking. One should start
by systematically doubting everything and find the first principle of
knowledge trusting only the procedures of logical thought. |
Descartes'
Cartesian philosophy of reference is expressed in the latin phase,
Cogito, ergo sum (l think, therefore I exist). This phrase is the point
of origin from which he derived the rest of the philosophy. Descartes
expressed Cartesian science in the establishment of the first principle
single point of origin from which he developed procedures by which to
study a three dimensional synthetic space and three dimensional virtual
objects inside that space, thus linking geometry to algebra and physics
to mathematics forever. Descartes did so by defining the Point of
Origin and procedurally referencing it to three infinite lengths of
cords called the coordinate axis labeled X ,Y, Z axis, that are
mutually perpendicular to each other and bisect each other at the point
of origin. The infinite axis having equal divisions of negative and
positive values which originate from a single point of bisection at the
point of origin.
|
 |
Therefore the
Point of Origin has a set of coordinate
axis values called coordinates of 0,0,0. Once the Point of Origin 0,0,0
has been established along the three axis, this creates the synthetic
existence of an infinite grid of cube shaped cellular space called the
Cartesian Coordinate Space.
This
synthetic space allows for the
development of mathematical modeling and the study of three dimensional
virtual objects. Rene Descartes' quantitative philosophy of synthetic
cellular reasoning succeeded in overthrowing a qualitative system of
natural reasoning philosophy of Aristotelian physics that was centuries
old. With Cartesian space (X,Y,Z), Function Representation (F-rep) - f
(X,Y,Z,...N), and the ever increasing computational power of computers,
we are ready to remove the rectilinear limits of virtual objects in
Cartesian space and model dimensions beyond our imagination.
The natural process of learning involves associating
new things to something that is familiar or looks similar. Visually a
line looks the same on a piece of paper as it does on a computer
screen. The comparison of a line on a piece of paper and on a computer
screen is the same as the comparison of a person who is dead and a
person who is alive. Please do not think that you will save time by
scanning the dead lines from paper drawings into digital alive lines on
a computer screen. This is much like trying to raise the dead. Yes, all
of the paper drawings you have are a thing of the past and need to be
made into models. The results of scanner / raising the dead will be
nightmarish zombies creating manufacturing horror stories equal to the
B grade movie "Night of the Living Dead". Remember the letter D in the
acronym CAD is for Design, not drafting. Thinking about using the
computer screen as a piece of paper is approaching the computer from a
2D drafting paradigm instead of 3D modeling, design and simulation
paradigm. So please resist the natural tendency to think of the the
computer screen as a piece of paper. Please think of the computer aided
design system as a cybership named CADesign and the screen, as
a windscreen, the face shield of CADesign through which you can
travel the vast reaches of multidimensional space. Refer to the CADesign's
process as modeling and the results as a model. A drawing is limited 2D
lines and paper attempting to fake 3D. If you are drawing with a
computer then you are using a paper design process that does not offer
the advantages of the digital design processes. A person, who is using
a calculator instead of CADesign's systems, drawing fake
dimensions on a paper screen, is not clear on the basic concepts of
using digital technology and therefore cannot see nor use the
incredible mathematical intelligence of CADesign's systems that
awaits their fingertips. Design calculations can be done easily by
using constructive modeling (the intelligence of CADesign's systems)
in
multidimensional
space.
By
watching
the calculations unfold before
your eyes, there it is on CADesign's windscreen if you dare to
explore constructive modeling solutions for a needed design
calculation. The use of constructive modeling on CADesign's windscreen
is
a
system
of
using
math visually. The proper use of CADesign's systems
allows
you
to access CADesign's mathematical intelligence
which mentors you in proper design replacing years of tedious
mathematical training. CADesign's command and control systems
has in line mathematical functions for all other calculations that can
not be solved constructively. CADesign's sixteen place internal
results does not need to be rounded off for the human operator. The
hand typed input from the eight place display of a hand held calculator
is some kind of a cruel joke. A designer/engineer at a CADrafting
workstation (a CPU with multiple parallel processing floating point
math units) using a pencil, pad of paper and a hand held calculator for
their design calculations is sadly unaware of the joke.
The word "Para" means
like something, but not really that something.
"Para Solid" modeling means its like solid modeling, but not solid
modeling. The base or core mathematical representation is not to be
confused with visual representation. Visual representations, wire frame
and surface polygonal meshes, are used to visualize the mathematical
representation. It is important to learn the difference between solid
constructive geometry, implicit surfaces, volume modeling and the
boundary representation polygon based procedures used by most CAD
systems. Early modeling systems were written complete with a user
interface, core processing and output routines by each company. However
many well known 3D CAD systems which claim to be "Solid Modelers" are
now constructed based on kernels obtained from third parties, notably
the ACIS (Spatial Technology, Inc.) and Parasolid (Unigraphics
Solutions, Inc.) kernels which only use some of the solid
modeling procedures. They typically do not retain any of the
mathematical primitives or history of procedures used, and the output
from these kernels are "polygonal meshes with holes" models. In fact,
they are boundary representations, not "solids". It is a fictitious
stretch of marketing imagination for most well known 3D CAD systems to
use the term solid modeler and to refer to the models created as solid
models. The so called "solid modeler" systems currently sold today are
most likely not!. Please note: ACIS and Parasolid kernels do allow
provisions for the retention of some type of procedural history. What
that procedural history includes is not clear and how the various
companies implement the kernels is not clear. A review of a recent
release of one CAD system shows that the " para solid models" can be
edited. This implementation of Parasolid shows a history tree of
operations. Mathematical representation by the "para solid" model
kernels are improving, but the models are still polygonal surface
models closely tied to the visual representation of the surface.
However because these improvements are not open for review, no one can
understand how good they are. Furthermore if they are closed systems,
they can not be compatible with other CAD systems.
| 2.4
Open
Procedural
History |
An open
procedural history or list of commands to create an entity is usually
much more compact than the completed model and is extremely important
to the migration of digital data to other systems. Furthermore, if
constructed properly, it contains all the information that is needed
for the final geometry, including the representations of solidity and
volumetrics. It has long been known that such a historical list
(actually a tree) of commands is a valid model in its own right. The
highly accurate input that forms an entity's history that can be used
to adjust the level of detail, and answer the same sort of questions as
the final model provides (e.g., is this point inside or outside the
solid?) without actually constructing a boundary model for visual
representation at all. The substantially significant advantages in the
use of procedural history include providing a robust data
structure providing stability and verifiable process procedure and
accuracy. Making a boundary based representation model is complicated,
and inevitably inaccuracies creep in; in particular, the edges of
a boundary model often deviate slightly from the surfaces that they are
bounding. It is extremely difficult to stop these errors from affecting
subsequent calculations. On the other hand, working directly from the
history with what we will refer to as a Constructive Solid Geometry
(CSG) model, we are using the 'raw ' input and geometry. The ACIS and
Parasolid modeling kernels of course use mathematical functions;
however it is anyone's guess what functions are used because the source
code is not open for peer review. Furthermore the vendors implement the
kernels differently. Most do not retain any history at all, but fool
their clients into thinking they are using "solids" and CSG when they
are not. Therefore without a history or a CGS procedural tree, most of
the models being created on most current modeling systems are dependent
on the system that created them and are subject to being lost when any
of the complex parts of the original system change. It is a sad fact
that most all of the 3D models without a history of procedures or
originating input could be useless within as little as one to five
years and, without a doubt, will not have any value in fifty. A
procedural history of the construction of 3D models is of key
importance to verify your 3D models, share your models between systems
and be able to migrate the 3D models to future systems, thus protecting
your investment of time and labor in creating the models.
 The six CSG primitives,
upon which Boolean operations can be
performed in CADesign.
| 2.5 Constructive Solid Geometry (CSG) |
Solid modeling
programs that have a proven set of mathematical operations and retain a
history of the mathematical operations and other procedures stored in a
CSG tree (that can be traversed and modified by the users to verify the
results) are recommended for many reasons. The following is an example
of the need to verify data using a CSG tree. The three-quarter view and
plan view diagrams below of a CSG tree of a solid model show the
model's primitives on a round pad, and the Boolean operations performed
on the primitives are shown on a binary fork in the branches of the CSG
tree. There are a total of nine primitives and eight Boolean operations.
 
The model's primitives
are made of eight cylinders and one cube. Starting from the top left
moving to the right and down in the bottom left diagram, the following
describes the union and subtraction of the first four primitives. In
the first two sets of cylinders with one horizontal and one vertical
cylinder in each set, the horizontal and vertical cylinders in each set
are joined together with a union operation to form two solid
cylindrical plus symbols. The small diameter shape is subtracted from
the larger diameter shape to form a hollow shape that resembles two
sections of pipe cut and welded together to form a plus symbol.
 
Theoretically with a
proven set of given mathematical operations, changing the order of
operations will always give the same mathematical results. However if
you look closely at the hidden view diagrams above of just the top part
of the CSG tree that has five primitives and four Boolean operations,
you will notice that the one on the left has different operations from
the one on the right. The one on the left has two Unions (U) and a
Subtraction (S), whereas the one on the right has two subtractions and
one union, in the first three operations. You will also notice the
last/fourth operation (at the bottom of the tree), a subtraction of a
cylinder, leaves an opening allowing you to see inside both of them.
You will see the hidden view of the one on the right confirms that the
model is not correct. Using the wire frame views of the models, you
will be able to see in the diagram below that the error actually starts
with the union operation previous to this one, but you cannot see the
error in the hidden view above. The modeling operations of the one on
the right is a more natural order of operations, using the subtraction
operations first to create horizontal and vertical sections of pipe and
then a union to join them together. However, this order of
operations creates an error as seen above.
Four wire frame
visualizations of solid models are shown above. The first wire frame
visualization of two tubes welded together starting at the top left of
the diagram is the result of subtraction of a two small cylinders from
two large cylinders creating two tubes followed by the union of the two
tubes into the geometric shape of a plus, and the wire frame
visualization clearly shows an error. The second wire frame at the top
right shows the subtraction of a fifth large cylinder through the
center of the plus shape and clearly shows that subsequent operations
carry the error forward, and the error grows. The third wire
frame visualization at the bottom left is the result of the union
operation of two large cylinders and two small cylinders into a large
and small plus shape followed by the subtraction of the small plus
shape from the large shape, and it is clear there is no error. The
fourth wire frame view, bottom right, is the result of the
subtraction through the center of the plus shape by a large cylinder
and clearly shows that there is no error. Again this type of error due
to change in order of procedures is clearly very wrong. The software is
quite flawed. In the future world of direct manufacturing, this type of
error will be unacceptable and must be discovered by design checking
agents.
Note: Do not assume your modeling to be accurate. The example above
shows that without understanding complex mathematics, you can visually
see the error in the model. The power to visually check complex
mathematical models is one of the greatest benefits of using CADesign.
The
solid
models
in
the
examples above were created using AutoCAD Rel.
12 software by AutoDesk with Advance Modeling Extensions (AME). AME is
the solid modeling extension of AutoCAD Rel. 12 and was one of the very
few commercially available solid modeling programs. AME and the CSG
tree were dropped by AutoDesk in Rel. 13. However, AutoDesk still
claims that AutoCAD Rel. 13 and beyond are "Solid Modelers" and that
simply is not true in this author's opinion.
| 2.7 Function
Representation ( F-rep) |
HyperFun
Project (http://www.hyperfun.org)
is
a
free
software
development
project for functionally based shape
modeling, visualization and animation. The project is based on a
so-called function representation (F-rep) (http://wwwcis.k.hosei.ac.jp/~F-rep/
)of geometric objects and supporting software tools built around the
HyperFun language. In F-rep, complex geometric objects are constructed
using simple ones (primitives) and operations on them. Any object in
three-dimensional space is defined by a function of point coordinates
F(x,y,z). This continuous real-valued function is positive inside the
object, negative outside, and takes zero value on its surface.
Similarly, a multidimensional object is defined by a function of
several variables F(x1, x2, x3, ..., xn). For example, an object
changing in time can be defined by F(x,y,z,t) with t representing time.
In HyperFun, the functional expressions are built with using
conventional arithmetic and relational operators, standard functions,
built-in special geometric transformations and F-rep library
functions.
HyperFun is the next step
in CADesign development, as it also allows the mathematical definition
of any number of attributes of an object such as materials, color,
texture, hardness, softness and so on. In creation of a CAD
system with HyperFun, the mathematical modeling will be retained apart
from the visual representation. Mathematical representation
being separated from visual representation and the processes open allow
the mathematical representation to be done on any platform now or in
the future. HyperFun has been in academic research and development for
many years, but the application side of development has just started.
At present, HyperFun modeling tools are still limited. There is not at
this time a robust user interface available. However development plans
to create synthetic CAD are underway and actual development should
start soon.
| 3.0 Technical Orientation |
In this section, we will discuss technical issues such
as the definition of the basic elements of a CADesign system,
CAD models, normal / natural orientation, mirror writing, CADesign
conventions in Cartesian space, wire model viewing, User Coordinate
System (UCS) icon.
A robust computer based modeling system creates a
mathematical model not a drawing. Therefore, you need the latest and
greatest computer you can lay your hands on. A plotter is necessary to
output paper drawings. You should always have a small printer
for data dumps to check files and operations. Do not purchase a tablet.
You only need a keyboard and a mouse. High resolution screens are not
recommended, because the lines on the hi-res screen become very thin
and cause eye strain. I recommend the Linux operating system and Varkon
CAD software (http://www.microform.se)
as
your
best
purchase.
For
rendering software, POV-Ray (http://www.povray.org)
is
great.
However it uses the left hand rule Y up, but uses the right hand rule
for rotation. You need to set up a transformation of the data to use
POV-Ray with your CADesign models which will be right hand rule
Z up. A review of Linux CAD showed it to be extremely poor. Also, get a
really good chair and make sure you have good support for your arms.
 |
A model, such as Sazaedo shown in the image to the
left, is
made up of objects which are made from blocks which contain entities.
Entities are the basic primitives of the system used to construct
blocks and objects. Depending on what are the basic primitives provided
by a given CAD system, entities might be points, lines, arcs , circles.
There is no standard convention for the naming of different elements
used in a given modeling system other than the naming conventions of
the Cartesian coordinate system. A point is a set of X,Y,Z coordinates.
A line has two points, a start point and an end point; so it has
direction and rotation; therefore a line is a vector. An arc can be
defined by a start point, midpoint, end point and has a direction of
rotation around the center point not to be confused with the midpoint.
A circle has a center point and a distance. A polyline has an unknown
number of points that define both lines and arcs. Polylines can be open
or closed entities. If a polyline is a closed entity, it can be
extruded into a solid object. Other basic entities are 3D faces,
polygons and polymeshes. Only three serious CAD systems have higher
level CSG entities. There are several experimental CAD systems that use
higher level function representation entities. From blocks or groups of
entities objects are created. In the Sazaedo model, the compound
complex shape of the lower roof could not be created with CSG
primitives. Also the spiraling over hanging roof and internal ramp
could not be created with CSG primitives, because they also have
compound complex shapes. Compound complex shapes have surfaces that
move in all three directions (X, Y and Z)at once. That is to say
that the X, Y and Z values for any given set of points on the surface
will be different. All other parts of the model including the top
roof are CSG based entities. |
IGES
(Initial
Graphics
Exchange
Standard)
and
STEP (International
Standard for the Exchange of Product Model Data) are standards for the
sharing of modeling data. However they are closed standards and, in the
IGES case, limited and, in the STEP case, not implemented. So
there is no standard data file format used in the CAD industry for
accurate three dimensional mathematical (CSG) models which can be used
to transmit the logical structure of the model, but only
disconnected surface data. The Sazaedo model is a
historical digital preservation work. Therefore, mathematical
definitions, accuracy of the model and a history of the logical
structure of the building are important information from the historical
preservation viewpoint. Only the CSG based entities will be able
to survive over time in the current CADesign environment. The AutoCAD
DXF, a DIF type file format, that has become a de facto standard for
the export and import of three dimensional polygon surfaces. The DIF
file format is type of binary file format. It is binary in that it has
two lines of text for each data record. The first line of text is a
code that tells what type of data is in the second line of text. Examples:
Code
0
is
the
start
of a new entity. Code 10 is the start point of a
line. Code 11 is the end point of a line. Most CAD files have data
tables of various settings for the operation of the system. The
settings necessary to setup AutoCAD for various applications can be
extensive. AutoCAD takes 250 keystrokes for the average setup of a
given application.
| 3.3 Normal / Natural Orientation |
In theory we can define
and use any orientation for modeling because mathematical
transformations are so simple and easy to do. Mathematical theorists
and some computer scientists insist orientation makes no difference if
the orientation is first defined. This is true in theory but not in
practice. Usage reveals that humans naturally establish one normal
orientation and can not think and work in different orientations
without experiencing confusion and making mistakes. The use of
orientations other than the normal orientation in theoretical work
obscures understanding and has even been used as a form of encryption.
Our hands are mirrored
structures of each other, and yet there are only a few exceptional
people who can easily handle or adjust to a stated orientation were the
input or output of a system is mirrored and rotated without making
mistakes. It is interesting to note that at an early age some children
are naturally ambidextrous and will easily handle writing with both
hands and can mirror write with either hand. To read what they have
written, one must hold the writing up to a mirror. However the children
see no difference at all, until it is pointed out to them and they are
taught the difference. Leonardo Da Vinci, an Italian Renaissance artist
persecuted for his knowledge and creative ideas, protected himself by
keeping his notes and journals from being easily read by mirror reading
and writing.
| 3.4 Mirror Writing Exercise
|
To understand
how important the use of proper natural / normal orientation is please
take out a piece of paper and pencil try doing the following tasks.
First, try writing with your left hand if your a right handed person.
If you are left handed person, you do not need to do this because you
live in a world of devices created for only right handed people. Now
please try some mirror writing with both the left hand and right hand
for a few minutes. Once you have tried the ambidextrous exercises, you
will understand how easy it is to get confused and how hard it is to
work in a different orientation. When possible, it would be better if
we all work with an established and agreed upon orientation, because
the confusion in trying to use different orientations is very great.
| 3.5 CADesign Orientation
Defined |
The
orientation in this chapter on modeling systems uses the Cartesian
Coordinate System having X, Y and Z axis with normal / natural
orientation. Normal / natural orientation is right handed where: the X
axis is positive movement to your right, the Y axis is positive
movement to the left , XY axis create a plane referred to as "the
plane" or "the ground plane" that is normal to the pull of gravity, and the Z axes is positive movement in the upward
direction, having vertical orientation to the pull of the gravity of
the earth and where the positive Z direction is against gravity. This
is the normal and natural orientation used in drafting, and CADesign,
because it is the orientation used in the fields of aviation,
engineering, architecture and manufacturing for the last four centuries.
Unfortunately some people do not have the ability to
visualize wire frames images in 3D at all. Working on wire frame images
from the bottom view is not recommended, because it causes visual
confusion as we shall see below. In working with wire frame, one
should use 3/4 views, which are 3D views, for designing and editing.
Those who attempt to design in "plan views" (views from the top)
or "elevation views" (views from the side) are not working in 3D, but
rather in 2D. They will have difficulty selecting a vertex,
because they will not be able to tell if the vertex is the one near to
them or far from them. However, plan and elevation views are useful for
checking the model. The following example shows the visual problems
associated with viewing a 3/4 view wire frame.
Which wire frame
view is from the top and which is from the bottom?
|
The
two
images
to
the
right
and the left are different views of a single 3D
model visualized in wire frame. The two views are of a rectangular box
that is 4 x 5 x 6 units in size that is a 3/4 view from the -1x -1y +1z
octant reveling the front, top and left hand side and a 3/4 view of the
same model from the bottom -1x, -1y, -1z. Please note: If the model
were a cube instead of a rectangle shown in 3/4 views from the
top (+1z) and from the bottom (-1z), we would see exactly the image.
Therefore we would not be able to tell the top of a cube from the
bottom of a cube. This problem is solved by using an icon to give
visual indication of orientation. |
|
Proper normal orientation is both the
visual and theoretical frame work on which you create a model. Modeling
with wire frame visualizations of complex mathematical models
is confusing at best and not even possible, if a standard normal
orientation and some type of visual cue for orientation is not used.
The "User Icon" is a dynamic symbol that is a visual cue for the user
as to the orientation of the User Coordinate System relative to the
World Coordinate System, the model and the user's view. The User Icon
indicates the location of 0,0,0 or the point of origin for the User
Coordinate System, the general orientation of the User Coordinate
System and the positive and negative orientation of the Z axis in
relation to the screen as shown below. Typically the User Icon is not
used in computer drafting which is 2D . This is unfortunate because the
ability to have access to a temporary point of origin / a user origin
point is extremely useful in designing in 2D. The default state for the
User Icon in AutoCAD is "on". It has been by the author's
experience that 95% of CAD installations do not use the User Icon; it
is turned off, as the users do not understand its function.
|
The
addition
of
a
coordinate
icon
helps. Now, can you tell which wire frame
is being viewed from the top and the bottom? If you can not, that is OK
because you can train yourself to be able to see wire frame 3/4 views
in 3D. A designer can not design in 3D if he does not turn on the
coordinate icon feature. Please note several things about the
coordinate icon. 1 - This icon displays a W and that means it is in the
world coordinate view. 2 - There are small tick marks at the
intersection of the two arrows; this means that the icon is on the
origin point. 3 - In the left hand view you will notice that two lines
are missing from the icon that form a square in the view on the right;
this means that Z is pointing away from you. |
|
Has the visual cues of the User Icon helped you to
tell which wire frame you are viewing from the bottom? Working
on wire frame images from the bottom view is not recommended, because
it impairs the user's ability to visualize the 3D wire frame model
without confusion.
Below are images
that show only six of the possible eight states of the User Icon's
visual cues. Two images are missing. Which ones are missing? Can you
list all eight states of the UCS icon? Read the three numbered
statements above again very carefully and you should be able to figure
it out.
| 3.9
Normal
Orientation
Exercise |
Three points
define a plane, a point and a line define a plane, and two lines define
a plane - are basic Euclidean axioms used in plane geometry. Using the
axiom two lines define a plane, we will create two 3D models of the X,
Y and Z axis of the Cartesian system - one with a sheet of paper and
the second with our right hand.
 |
1st model
Take out a sheet of paper and thin wooden pencil. Now place a point in
the middle of the paper and label it O for origin. Now draw a line from
the origin point in the direction to your right and label it X. Now
draw a second line from the origin point perpendicular to the first
line in the forward direction and label it Y. With these two
perpendicular lines, the first plane of the Cartesian system called
"the plane" is made. The term "the plane" always refers to the X, Y
plane or ground plane that is normal to the pull of gravity. Now finish
the representation by piercing your paper from the back side at the
origin with the point of your pencil pointing upwards from the front
surface of the paper normal to "the plane". Please be careful -
but look at the paper with the point of the pencil pointing toward you
so it looks like the image to the left. In drafting, this is
called the default view or unless otherwise noted the top down or "plan
view" of "the plane". You might think of this view as a map or a layout
of the ground plane with you in the center. This is the creator
orientation or "God Orientation". Place this model in your
left hand and create the second model. |
2nd model
Now, hang your right hand downward with hand open and your fingers
pointing toward the ground plane. Next, rotate your wrist so that the
palm of your hand is facing in the forward direction. Bend your right
arm at your elbow 90 degrees so that the palm of your hand is now
facing upwards. Your right hand and your thumb should be pointing in
the positive direction of the X axis or movement to the right and your
index finger is pointing in the positive Y axis or pointing forward.
Now, bend the third finger upward. It is now pointing in the Z
axis. Rotate the right arm at the elbow so your right hand is
directly in front of you just level with your elbow and keeping your
right hand as shown in the image. In 3D design, this is "the
view", "the artists view" or in drafting "the three quarter
view". "The view" is the normal viewing of real objects that is
the most common view experienced by people. It is a view of an object
from a natural body position for normal people. Now move and
rotate the paper model to a position that is the same orientation as
your right hand. This is the "Right Hand Rule". |
 |
The above 3D models, one with paper and pencil and the other with the
right hand, are anthropomorphic based orientation for 3D modeling and
viewing - that is most efficient for humans. In fact, if you do
not use this view, you probably will not be able to model in 3D.
This orientation is called "the right hand rule" with the normal
natural orientation of Z up (Zup). However Zup is the not the natural
orientation
for
some
people
like
programmers. They work visually
in a virtual world of a computer screen where the forward movement of
the mouse in the real world is transferred to an upward movement of the
mouse cursor. So the natural orientation for them is Y up (Yup).
The difference in orientation between the Yup people and the Zup people
causes conflict. Orientation confusion in the real world where gravity
is a serious matter can lead to serious mistakes.
| 3.10 Virtual World
Orientation |
Virtual
world
orientations
are
in
conflict
with the real world. Unfortunately
the orientations used in virtual worlds are not just the relatively
simple Zup Yup conflict of a 90 degree rotation, but the virtual
orientation is often mirrored from right to left as well. Programmers
who spend most of their time viewing and navigating the abstract
virtual world of cyberspace and very little time building physical
things in the real world of gravity are not aware of right handed
orientation or the need for a person modeling to read wire frame models
with normal views that match aviation and engineering standards. Such
programmers have written all of the basic Open GL libraries (http://www.opengl.org) with the
virtual world orientation of left hand rule and Y up. Novice
programmers who are not aware of the problem will of course write
simple programs using the the left hand rule Y up orientation of the
Open GL libraries. A very famous program, POV-Ray, uses the left hand
rule Y up orientation and the right hand rule for vector rotation. VRML
(Virtual Reality Modeling Langauage) uses the orientation of right hand
rule and Y up, and the HyperFun program began life with the left hand
rule Y up orientation. HyperFun, looking toward synthetic simulation,
did not want to be in conflict with the real world and modified their
orientation. The Y up (Yup) or Z up (Zup) problem is the most difficult
to change in computer science because all the books about Open GL talk
about the Z buffer as a depth buffer, which has become standard
nomenclature for the virtual world. Open GL libraries were given the
orientation left hand rule with X as width, Z as depth and Y as
vertical height. These alternate views are placing serious barriers to
the visual bridge between the real and virtual worlds and causing a
great deal of disorientation and confusion. Mirrored and rotated
systems, including VRML standard language and POV-Ray, come from not
trying to find a first principle with regard to normal orientation in
the real world. People creating such systems usually start out by not
being aware that their virtual world orientation is in conflict with
real world orientation conventions of the last 400 years in
engineering, manufacturing, and aviation. Programmers continue to use
the left hand rule which is a mirror of the right hand rule and/or a
Yup orientation which is a 90 degree around the X axis from the real
world normal orientation of Zup.
The following is a quote from the POV-Ray web site:
"there is so much controversy about the right hand rule we
decided to use the left hand rule"
The X, Y axis
divides a given space into four sections, called quadrants. The
addition of the Z axis divides the quadrants to create octants.
|
If we pick a
point O as origin and draw two perpendicular lines through the origin,
we create "the plane." The two lines are labeled X and Y axis. The term
"the plane" always refers to the X, Y plane or ground plane that is
said to be horizontal to or normal to the pull of gravity. In the
practice of drafting, the default view shown to the left is the view
from the top down or "plan view" of "the plane." You might think of the
plan view as a layout or a map of the ground plane. The plane's X, Y
axis create four divisions of coordinate space called the "quadrants."
The quadrants are named for their signs. The 1st quadrant is called the
plus plus quadrant (+X +Y axis). Proceeding in a counter clockwise
rotation, the 2nd quadrant is the minus plus quadrant (-X +Y axis). The
3rd quadrant is the minus minus quadrant (-X -Y axis) and the 4th
quadrant is the plus minus quadrant (+X -Y axis). A move to the right
is in the positive direction of X. A move to the left is in the
negative direction of X. A move forward is in the positive direction of
Y. A move backward is in the negative direction of Y. |
| The third axis,
the Z axis, is added mutually perpendicular through the point of origin
of the X, Y axis. The a third dimension Z is know as height or
elevation in aviation. The Z axis creates eight divisions of three
dimensional space called "octants." The positive direction of the Z
axis is up against the pull of gravity. Adding the Z axis defines two
more datum planes, the X, Z and the Y, Z. When viewing these datum
planes from a perpendicular angle to the surface of the planes, the
views are refereed to as plan elevation views in the fields of
engineering, architecture and aviation. The figure to the right showing
all of the octants is known as a 3/4 view. Now we have created a
synthetic space, and every point in that space has a unique triplet of
cartesian coordinates labeled as X, Y, Z . It is understood that if
given a list of three numbers, they are the Cartesian coordinates X, Y,
Z - - and they are used to determine a point in Cartesian space
applying a number as movement in space along X, Y, Z axis. The 1st
octant is +X +Y +Z. The 2nd octant is -X +Y +Z. The 3rd octant is -X -Y
+Z. The 4th octant is +X -Y +Z. The 5th octant is +X +Y -Z. The
6th octant is -X +Y -Z. The 7th octant is -X -Y -Z. The 8th octant is
+X -Y -Z. |
 |
| 4.0
Cartesian's Navigation Systems |
In this
section we discuss the subject of Cartesian navigation or viewing
in-depth. Examples below will show you how to view and change views of
multidimensional models in the virtual space created by the Cartesian
coordinate space system on the windscreen of your computer modeling
system. ("Cartesian's windscreen" where Cartesian is the
name of a new imaginary multidimensional spacecraft to be constructed.)
We also present an imaginary user interface to describe the subject of
viewing in-depth in the text below, as if it were an existing command
where the use of two letter acronyms is the keyboard entry which brings
on screen "Cartesian's" visual interactive interface for the
command mode. The ease and skill with which one can view the
development of a 3D model is an essential part of being able to model
in Cartesian space. A person's modeling ability is only limited by
their ability to navigate Cartesian space. Exploration and development
of effective navigational systems for Cartesian space has just begun.
The complete user control and ease of navigation in Cartesian space is
the most important aspect of multidimensional modeling.
We will begin
with an outline of all of the parts necessary for a robust Cartesian
based navigation system and then discuss the addition of a
multidimensional interface to navigation systems. Modeling systems must
define and keep track of at least two Cartesian coordinate systems, the
world and a user view. Most robust systems track and use at least four
to five different types of coordinate systems:
- World
coordinates
- User
view coordinates
- User or
creation coordinates
- Entities
coordinates
- Groups
of entities coordinates
| 4.2 World Coordinate System
(1) |
The World Coordinate
System is a single point of origin / base / handle / for the entire
model and for the other coordinate systems. However it is possible to
create a simple system using only World and User View Coordinate
System(s). An example of this type of system is the HyperFun
polygonizer; such systems most usually depend on mathematical
definitions and are important teaching tools that provide an intuitive
feel for the relationship between math, geometry, programming and
computer visualizations. These types of systems are not useful for
modeling large complex objects or designs, because they are text editor
based. Viewing from only one View Point (VP) and the point of focus or
the View Target (VT) will allow us to easily see and verify the results
editing a single simple object using a text editor, as shown in the
HyperFun example below. To do visual based editing rather
than text based editing, one needs the other coordinate systems as well.
HyperFun (http://www.hyperfun.org)
is
a
simple
system
of
navigation for simple constructions. However, in
concept, the system can mathematically model any level of detail.
Text File
|
HyperFun uses one and a half (1 1/2) coordinate
systems. The
world coordinate system is almost the same as the the view target (VT)
or point of interest. The user can not move the VT or point of interest
and therefore is unaware of it. Only the user view point can be moved
by the user.
 |
VT - point of interest can not be moved. This system
can not
be used for large models with many objects. The text file is shown to
the left. Next to that at the command prompt, the program is called by
"hfp txt.hf -g 35" and the image of the model appears in the foremost
screen shot. The user view can be rotated and zoomed with the mouse. |
The VT (point of view) is just off center
from the world coordinate system so that when the user view is rotated
around a sphere, some movement is able to be detected due to this
slight offset.
|
The User
View Coordinate System is usually defined by one point, a direction or
point of interest and rotation that creates a cone and plane of view.
This
is
needed
so
that
the user can change views and work from various
viewing angles. The editing of a single object can be done
interactively on your windscreen using the rendered visualizations of
the object. However when you use the visualization to edit even a
single simple object, it is done much more efficiently with the use of
wire frame visualizations (X-ray vision) rather than solid rendered
visualizations. While seated at Cartesian's controls, you can
issue a command for a re-scanning of the mathematical model. You can
either use normal vision and view the solid object, or you can give
yourself Superman's X-ray vision and render the Cartesian object
transparent so that you can see all boundary points and edges.
solid visualization |
X-ray visualization |
| 4.4 Superman's X-ray Vision |
A 3/4 view from 225 degree & 35.8 degree
|
Using X-ray vision provided by Cartesian's
windscreen
conveniently and efficiently allows you to make interactive
mathematical modifications to the object. Cartesian's digital
agents do the calculations for you. However, when you use X-ray vision,
you are using a very unnatural view, and, as shown to the left, certain
X-ray viewing angles (even simple ones) can be very confusing and
almost impossible to utilize. The image on the left is a wire frame
model of 3D cube of 5x,5y,5z units. It looks like a flat 2D six sided
figure. Can you visualize the image in 3D and see it as a cube.? A
solution as mentioned before is the use of a user icon. However it is
very hard to read upside down, and with many complex models the icon
becomes difficult to use. The icon helps but by itself alone is not a
good solution. Therefore it is necessary (when using X-ray vision to
edit objects) to be able to easily understand your orientation to the
objects and the surface and distance relationships between the objects
being viewed. |
| 4.5 Autonomic Autopilot Controls
|
|
Cartesian's
autonomic autopilot controls will
have autonomic movements, surface probing , and visual acuity systems
with standard tele-transport positioning portals. We will describe only
two of the proposed navigational controls all ready proven to aid your
visualization processing of wire frame models. One is the use of
autonomic movements or (very slight rhythmic real time changes in the
user view). All living creatures have continuous autonomic movements
that aid the creature's perception. The second is the use of standard
View Points (VP) so that you may instantly tele-transport to a position
in Cartesian space. Below are the
proposed four standard 3/4 views for modeling in three dimensions. The
first view is "the view" V1 shown on the left. This is the approximate
view point of a person viewing an object in their right hand with:
elbow bent at a 90 degree angle, the palm up, hand open, the front of
the object aligned with the X axis of the thumb, the arm rotated so the
object is directly in front of the person's waist.
- View 1 (V1) is a VP from the 3rd or ( -
- +) octant.
- View 2 (V2) is a VP from the 4th or ( +
- +) octant.
- View 3 (V3) is a VP from the 1st or ( +
+ +) octant.
- View 4 (V4) is a VP from the 2nd or ( -
+ +) octant.
|
 |
Note: The 1st (+++) & 5th (++-) octants are used
for modeling space. The 5th (++-) octant is for objects that are below
ground level.
 |
VP V1 is a common and familiar natural viewing of an
object,
because it is a viewing point as if the object were being held in your
hand. We will call this "The Normal View" to the plane. V1 is said to
be the most normal (as in normalcy) because it is the most common
familiar natural viewing of an object as experienced by most people.
"The Normal View" turns out to be extremely important, because it is
the best angle for X-ray viewing of a 3D model without experiencing
visual confusion. The parallel to the ground plane viewing angle of
normalcy for VP V1 from the ground plane is 35 degrees plus or minus 10
degrees. VPs V2 V3 and V4 are less normal than V1, but are very good
angles for X-ray viewing also. VPs V1 V2 V3 and V4 establish a normal
cruising range for viewing a object while modeling. A person modeling
tries to keep the view as normal as possible to avoid visual trouble.
The dial gauge type diagrams at the left give a read out in degrees of
angle for user view point V1 and also show the angles of V2, V3, V4. |
| 4.7 Rotation of User View |
|
View One (V1)
|
View Two V2
|
In
the
images
to
the
left,
the user view is rotated - the object is not.
The object is not moving in relationship to the World Coordinate
System. If the User Icon is not turned on, there is no way to know if
the view is being moved or the object is being moved . The novice user
who usually turns off the User Icon, not understanding its importance,
becomes confused and lost between the movement of the View Point and
the movement of the object. |
|
View Three (V3)
|
View Four (V4)
|
The
object
is
rendered
to
avoid
visual confusion. However one needs to use the hidden
lines (lines that have been hidden from view) during the modeling
process. Therefore, rendering is for visual verification only
- not to be used during the actual modeling of the model.
Please note: The View Target 0,0,0 is
laterally moved in the images shown to the left using the pan or the
zoom window command. |
There
is some normalcy in
viewing angles. However you might have noticed by now that we have only
moved the View Point VP and not the View Target VT. VT remains
unchanged; this is unnatural and strange to most people and hard
to get use to at first. You can experience and understand how strange
this is by walking around a room keeping your head and eyes on one spot
(the VT) in the middle of the room. The only way to move the VT point
is to pan or zoom to an object. However when you rotate the VP,
the VT point moves back to the origin point 0,0,0 zooming out to the
extents of the model, requiring the person modeling in 3D to zoom in
selecting with a window an area to zoom into. In a large model, this is
a very slow process for the computer to regenerate an image of the
entire model, then the window selected. A nightmare exclaims! the
person translating this text who has had no experience with CAD. Why?
someone might ask. The answer is: The indirect movement of the VT in
current CAD system interfaces is a 2D drafting legacy. The interface is
a 2D paper interface. This viewing is not so strange or unnatural to
the drafting person who works on flat two dimensional drawings. His/her
viewing angle is "normal" or 90 degrees from the surface of the paper
on which he works. The use of a paper interface by current CAD systems for 3D
modeling
is
irritating
at
best,
though it does allow the construction
of large models with many objects. In the real world, the user VT point
is always moving (the turning of your head), whereas the user View
Point is more difficult to move - you must move your body.
| 4.9 Navigation Conclusion |
The
development of a CAD interface from drafting standards is a force and
fake application of paper drafting design applied to digital design. A
true digital design interface has little or nothing to do with
drafting. When a 3D model is complete, it is sometimes projected into a
2D surface model where some drafting types of operations are applied
for additions and adjustment in order for the 2D projection to be
printed on paper. The current CAD interfaces with the paper like
qualities are unlike
that of game simulation movements that provide a natural interface; it
is very easy for a user to quickly understand how to navigate in a
simulation system. A simulation game type system of navigation is
proposed as the core of Cartesian's control
system.
The pure visualization power of "Cartesian's windscreen"
stemming from the qualities of digital material has no equivalency to
the visualization capabilities of paper materials and processes.
However a subjective personal comparison can be made about interactive
digital and paper based processes. Sitting at Cartesian's helm
with digital agents at your command is much more exciting, rewarding
and enjoyable than sitting at a computer used as a substitute for
pencil and paper. Trying to fit paper processes into the digital world
is not much fun. Now sitting at a drafting board using simple tools and
materials to hand create a drawing has a calming, meditative aspect
that is very enjoyable, but it is not as efficient nor as precise as
digital based design processes.
The common starting assumption for novice users and designers of CADesign
systems is that of a "new clean sheet of paper," i.e. a blank
screen; unfortunately this is a paper legacy concept that is misleading
in the digital environment . Digital systems are based on sharing and
modifying pervious work. Unfortunately the CAD (drafting and design)
world is very slow in becoming digital because of patents and
copyrights. So, the sharing of models has not become prevalent or
technically high level. However, "reuse" was one of the basic reasons
behind CADesign systems, since they allow creation of blocks
of parts, save them and insert them into different models. It was
thought that digital based designs would be much more persistent than
paper designs, because digital data does not degrade when copied or
wear out like paper. However, digital data persistence has turned out
to be a big problem for complex reasons not covered here. The starting
assumption should always be - - to start a new model based on a
previous model or parts, that creation is the evolution of existing
models. In the author's seventeen years of consulting and installing CADesign
systems, the creation of base prototype models to create new models was
the key to any client's success. After several years of using a CADesign
system, you may come to realize that the moving, rotation and editing
of models are the most used and important modeling and design functions
in the CADesign system. However, in general, the most current CADesign
systems are designed for a "new fresh blank screen," because
programmers who design CADesign systems do not use them for
long periods of time in production oriented environments. What is:
digital material? digital culture? and digital arts? "What does it mean
to be digital" is key to being able to successfully apply digital arts
to the design process.
| 5.1 User Coordinate
System (3) |
The User Coordinate System is where creation/editing is done. It can be
viewed as a local coordinate system created for the ease of editing
objects in space. It is the space you are viewing through "Cartesian's
windscreen." In single object models, the user coordinate will be the
same as the World Coordinate System, but in large models, almost never
the same. The proper normal position for the User Coordinate System
during the creation of an entity using a "god orientation" is the
following: the X axis origin starting point is placed at the lower left
front, the positive direction of the X axis is to the lower right front
and the Y axis positive direction is down the right side of the entity
and Z is up. This is extremely important, because the User Coordinate
System position during the creation of an entity becomes the Entity
Coordinate System.
The following
is the movement of objects in relationship to the World Coordinate
System. The movement along the X, Y, and Z axis is repeated by two key
commands entered at a command line prompt. Motion studies show that
using the command line prompt with one or two keys representing the
command followed by the space bar as an enter key is the quickest form
of entry possible at the present time. However, a virtual reality
interface with the use of first person tools may represent even a
faster from of command and control for modeling systems of the future,
a far more intuitive interface.
Move Right (MR) is +X
|
Move Left (ML) is -X
|
Move Down (MD) is -Z
|
Move Forward (MF) is +Y
|
Mover Back (MB) is -Y
|
Move Up (MU) is +Z
|
Commands to move an object are the following: Move the block to
the Right (MR) moves in the positive direction of X; Move
Forward
(MF)
moves in the positive direction of Y; Move Left
(ML) moves in the negative X; Move Back (MB) moves in
the
negative
Y;
Move Upward (MU) moves in the
positive Z; Move Down (MD) moves in the negative Z.
Please note that the move commands above are from the current
position and rotation of the UCS. The move command is used very often;
it is more convenient to think in right, left, forward, back, up and
down. Note the movement is based on the user's orientation or "god
orientation" not the entity's orientation or "actors orientation." The
Move Right command in the command line mode looks like this at the user
prompt:
MR in the <P>lus / Neg <X> /Y/Z axis by the
EditNumber (EN) / <9.999999999> or select:
Objects <P>revious/1/2/3...or select:
| In CAD positive
rotations are counter-clockwise around a vector if the positive
direction of the vector is pointing toward you. In CAD a line has a
start point and an end point, i.e. direction or vector and the positive
rotation around the vector follows the conventions of the right hand
rule. To help you find the positive rotation of a line using your right
hand, follow the directions below:
* Open your right hand
* Stick out your right thumb
* Aim your right thumb in direction of the end point of the line
* Curl the fingers of your right hand around the line
|
 |
The direction of the curl of your right hand fingers around the line is
in the positive rotation. The uncurling of your right hand fingers is
in the negative rotation.
+ Rotation X axis (RX)
|
+ Rotation Y axis (RY)
|
+ Rotation Z axis (RZ)
|
The rotate commands by
default rotate in the positive direction or Counter
Clockwise (CCW) direction. The negative direction is a
Clock Wise (CW) direction. The Rotate
command rotates objects; it does not rotate the view or the Cartesian
Coordinate System. The rotate commands are as follows: rotate
the block around the X axis is (RX); rotate around the Y
axis is (RY); rotate around the Z axis is
(RZ). Please note that the rotate commands above are from the
current UCS position. The images above are from the WCS, but could just
as easily have been from some User Coordinate System or an entity
coordinate position. The single key command ( R)otate provides
the user with rotate mode options that become defaults for the RX, RY,
RZ commands. Rotate is not used as much as the move command. The Rotate
command in the command line mode looks like this at the user prompt:
RZ = X/Y/<Z> axis Neg/<P>lus by
Entity/World/Current <C> by <90>:
Objects <P>revious /1/2/3... or select:
| 5.5 Entity Coordinate System (4) |
The Entity Coordinate System is really an entity creation coordinate
system with a "god orientation," which is the position of the User
Coordinate System when the entity was created. The "god orientation"
being the orientation of the user / creator's right, left, forward,
back, up and down. Entity Coordinate System is not really properly
named, because it is really just the position of the User Coordinate
System given to the entity for the convenience of editing in CADesign
systems and is really just a way to move back into a convenient
modeling / creation position. In animation systems, the entity / actor
has its own "actor orientation" system which is moved from the lower
left hand corner of the entity to the center of the actor, and the
Entity Coordinate System is rotated 180 degrees from the "god
orientation" to the "actor orientation." In animation systems, the user
/ director directs the movement of an entity / "actor orientation"
using the entity / "actor orientation" rather than the "god
orientation." This feature is very convenient for
animation. Animation systems also have creation systems, in which
unfortunately they continue to use the "actor orientation" which is not
easy to use for the creation of an entity. The use of both
orientations, the god for creation and the actor for object movements
in one system, turns out to work very well. You might notice for this
chapter that the move command uses the "god orientation" to avoid
confusion of mixing systems in theory. However, in real applications
the mixed use of both the god and actor orientations is quite natural
and actually avoids confusion. Depending on the CAD
system chosen, you may or may not have access to the Entity Coordinate
System. Most people are not aware of this system or its different
orientations. However it is a very powerful system and will be one of
the core systems necessary for Cartesian's navigation and
visualization systems.
 |
Alice (http://www.alice/org) is a 3D
Interactive Graphics Programming Environment for Windows 95/98/NT built
by the Stage 3 Research Group at Carnegie Mellon University. The Alice
project is a public service to the wider computing and artistic
communities. The current version of Alice authoring tool is free to
everyone and runs on computers that are commonly available for
reasonable prices. Worlds created in Alice can be viewed and
interacted with inside of a standard web browser once the Alice plug-in
has been installed. Alice is primarily a scripting and
prototyping environment for 3D object behavior, not a 3D modeler;
this makes Alice much more like LOGO (http://el.media.mit.edu/logo-foundation/logo/turtle.html)
than
AutoCAD.
By
writing
simple
scripts, Alice users can control
object appearance and behavior, and while the scripts are executing,
objects respond to user input via mouse and keyboard.
You can create 3D models using a web browser with
Teddy2. Alice runs Teddy2, a sketched based 3D modeling tool
developed by Takeo Igarashi at the University of Tokyo. During
the creation process, the "god orientation" is used. However, at the
end of the process when you save the model, Teddy2 has you orient the
front of the object to face you. Saving the model in that
position gives the object the "actor orientation" shown in the image at
the left. So objects in Alice have their own sense of direction.
This makes the control of the object very easy. Try loading Alice and
using their tutorial to create a 3D object by sketching.
|
| 5.6 Group Coordinate
System (5) |
Every group
or block of objects has an insert point or base point assigned to it by
which to insert, move or rotate it as a group. This coordinate system
is an essential system. Without this system, one can not insert a model
or part of a model into the model being worked on. It is the system
that turns all of the rest of the models into a library of parts or
blocks that can be used repeatedly. It is a digital extension of
yourself that you can share digitally with others and giving you value
in the digital world. Digital modeling is part of the growing landscape
of digital containing digital swarms of information ... to be used from
any location on the Net.
Knowledge
provided in this CAD chapter is a summery of twenty years of experience
in computer aided design. Much of the information contained here is not
found in any other educational texts of which I am aware. The goal of
this chapter is to transfer the knowledge needed to set up a digital
framework for doing the exercises below and teaching yourself a CAD
system of your choice. It would be a waste of my time and yours to
present knowledge, information, and exercises that are common place and
can be found on the WWW easily. Instead I urge you to access that
easily found information yourself using the WWW. Learning the line,
circle command in one particular CAD system is best done by yourself
using that particular system's online help and tutorial. What is
missing from the online help systems is why and how to apply digital
systems to 3D design. I have found only one such book, AutoCAD 3D
Design and Presentation, M. Bousquet and J. Hester, New Riders
Publishing, Carmel, Indiana, USA (1991) ISBN 0-934035-81-4. Though it
does not have an educational focus or an overall approach, it does give
step by step procedures for AutoCAD as a 3D design system. Follow the
exercises below and you will be well on your way to CAD mastery.
Exercise 1
- Take out a piece of paper and pencil.
- On one half of a sheet of paper, draw the Cartesian
Coordinate System's X, Y, Z axis from the - - + view (V1).
- Divide the axis in the positive direction into 10 equal
segment starting from the origin point.
- Label the drawing with the first principle of Cartesian
existence.
Exercise 2
- Using the axis drawing from Exercise 1 - construct a 4,5,6
unit size box on the axis starting at 0,0 * Tip: Graph out the
following points on the axis drawing and then connect the lines:
0,0,0 4,0,0 4,5,0 0,5,0
0,0,6 4,0,6 4,5,6 0,5,6
- Label the eight corners of the 4,5,6 box
- Relative from point 4,5,6 - place a point at 4,4,4
Exercise 3
- Install a CADesign program of your choice on a
system of your choice.
- Create a 3D model of the paper drawing done in Exercises 1
and 2.
- Reflect on and evaluate the CADesign software
program.
Exercise 4
- Load Alice and use Teddy 2 to sketch a soft object /
toy. http://www.alice.org/
- Load FreeCAD - use the tutorial and evaluate the addition
of reverse kinematics to CAD. http://www.askoh.com/
- Load HyperFun - use the HyperFun tutorial and evaluate the
concept of F-rep. http://www.hyperfun.org/
Exercise 5
- Get a package of Lego blocks and calipers with LED read out
and make precise 3D models of them with a CADesign of your choice.
|
|
