MacWireFrame
Volume Number: 7
Issue Number: 11
Column Tag: Tools of the Trade
MacWireFrame & Desktop Lawyer 
By Dave Kelly, MacTutor Editorial Board
MACWIREFRAME 3-D Graphics
Amplified Intelligence has recently released their three-dimensional graphics
library for THINK Pascal. The MPW Pascal counterpart has been available for some
time now. The package includes a sample application program, MacWireFrame that
illustrates the capabilities of the 3-D library.
MacWireFrame is a wire-frame editor used to create three-dimensional
wire-frames. A wire-frame is a mathematical term used to describe a
three-dimensional object formed by lines or wires. The wire-frame lines or wires
represent the path between two vertices.
The source code supports five key data types. By understanding these data types,
you will be ready to use the MacWireFrame library.
MacWireFrame uses linked arrays to represent rotation and scaling matrices,
translation vectors, three dimensional points and lines in space, two dimensional
points and lines in planes and view matrices used to transform three dimensional data
into two dimensional data. These linked arrays are dynamically allocated array
elements that consist of a handle to a record containing a real number and handles to two
other linked array elements (the next row element and the next column element).
MacWireFrame performs matrix multiplication on linked arrays to accomplish
rotation, scaling and mapping from three down to two dimensions.
A spacepoint is an array of three real numbers: the X, Y, and Z coordinates of a
point in space. A spacepoint is the basic building block of wireframes. The
MacWireFrame manual explains the spacepoint type in an amusing way:
ABOUT SpacePoint
“SpacePoint = array[13] of REAL;”
“The single line of code above really says a lot about our universe. It says that a
point in space is defined by three real numbers.”
“Once, back a long time ago, I was walking into the cafeteria in high school when
I noticed that the nerd crowd was having a heated argument and, being a troublemaker, I
went over to start trouble. I quickly learned that they were arguing about whether it is
possible to assign a real number to every point in space.”
“Why not ask my smart friend, Dave,” I thought. Dave was one of my high school
buddies who later went on to get a Ph.D. in Physics and became a physics professor. I
began to explain the problem to Dave: Say that you started out with one line in space and
started assigning numbers to it. By the time you were done, you would have used up all
the real numbers and wouldn’t have any left over for any of the other points in space.
“Yes,” my friend Dave answered, “but what if, instead of a straight line, you used a
single squiggle line that went around all over the place until it eventually hit every
point in the universe?”
“This same type of problem has vexed mathematical thinkers since the beginning
of Man. In fact, according to legend, there was once a cave man named Grunt, who lived
back in the days when math was a lot more simple. People back then would count by
saying, “one, two, three, many.”
“For example, Grunt had two wives and many children. On one of his recent
hunting trips, Grunt had killed two deer, one antelope and many jack rabbits. Back
then, numbers above two to the second power were so rare that, for most practical
purposes, it didn’t make any difference just exactly how big they were -- kind of like
numbers larger than two to the thirty second power are today.”
“But then one day Grunt began to think about mathematics. Near Grunt’s cave
were two piles of rocks, and although each pile had many rocks, Grunt began to wonder
which pile had more rocks. Grunt wished that he could first count the number of rocks
in one pile and then count the rocks in the second pile, so that he could find out which
pile had more rocks, but he lacked the mathematical sophistication to do this.”
“For awhile, Grunt and his friends sat around arguing about which pile of many
rocks actually contained more rocks than the other, until finally Grunt came up with an
idea. Grunt thought, “What if I take one rock off the first pile of many rocks and then
one rock off the second pile of many rocks and keep doing this until finally one of the
piles has all it’s rocks used up. Then at last, I will know which pile has more rocks.
Grunt had discovered the mathematical concept of a one to one correspondence.”
“Of course, each pile of many rocks had many rocks in it and Grunt soon got tired
and hungry and went off to pick berries before he ever really found the answer to his
question, but never the less Grunt had had a brilliant idea.”
“The first line of code in the MacWireFrame Editor uses only slightly more
complicated thinking. A Mac II computer with its thirty two bit registers can only
comprehend numbers up to two to the thirty second power. There are a lot more points
than that in the universe and a lot more points than that in the theory used by the
MacWireFrame Editor.”
“There are more points in the universe than there are real numbers. This might
be hard for us to understand today because infinity is somewhat more of a difficult
concept today than it was in Grunt’s day. Infinity really means “so many that it is
theoretically impossible to count”.
“What the first line of code in the Editor says to the computer is that there is a
one to one correspondence between every point in the universe and every possible
ordered triplet of real numbers”.
A vertex is a three-dimensional point in space that is connected to three other
vertices by lines or wires. It is one of the key building blocks of a wire-frame. A
vertex consists of a spacepoint and an array of handles to three other vertices. A
wireframe is then built from an interconnected set of vertices. Representing
wireframes as interconnected vertices has numerous advantages. The most spectacular
of these advantages can be seen while doing three dimensional dragging. If you select
some of the vertices in a wireframe and drag them while leaving the others behind, the
connections between the selected and unselected vertices will stretch like rubber bands.
Another advantage is that since vertices are linked with handles to other
vertices, operations need to be performed only once instead of three times. This is
because when drawing a vertex alone, you would draw the three lines that connect to it.
Since the vertices are linked to each other, it is not necessary to draw the lines twice.
This makes the operation much more efficient.
Some surface models based on polygons claim to have wireframe capabilities, but
each line in a wireframe is associated with at least two polygons in a surface model so
the same operation done to an interconnected set of polygons takes six times as long as
in MacWireFrame.
A pointlist is a linked list of vertices. This type comes in handy for performing
operations on vertices because of its linear nature. Vertices have three ways to go from
any given vertex, but on a pointlist, there is only one.
An entity contains all information needed by MacWireFrame to maintain the
display interface. There are five windows available in MacWireFrame: isometric, top,
front, side and custom views. An entity maintains the relationship of these views. In
addition, an entity type contains a field that keeps track of which vertices are
highlighted.
A space point is a field in the type vertex which is a field in the type pointlist
which is a field in the type entity. Thus an entity represents all of the space points and
vertices in an object. The wireframe entity shown in the figure is made up of two cube
objects. The smaller one was scaled copied and pasted on top of the larger one using the
MacWireFrame editor.
Both ends of a wire-frame wire or line is tied to a vertex. The wires are
straight (no curves) and have no hidden lines. Thus, you can see that every vertex has
three lines attached to it and all of the lines and vertices make up the entire entity.
The MacWireFrame application allows you to create wire-frames based on a cube
or a tetrahedron. From there, you can add or remove lines, rotate the object, rotate the
vertex, scale the object, scale a portion of the object, translate an object or drag the
object with the mouse. A dimension dialog can be used to tell you the distance between
two highlighted vertices of an object. TransformObject is the function at the heart of
MacWireFrame that makes things tick. You give the TransformObject function a
pointlist and a predefined linked array. The function looks at the size and if it is a
translation vector then it will add the vectors to each point on the list thus
implementing translation. If the matrix is a 3X3 matrix, then TransformObject will
matrix multiply each spacepoint on the pointlist thus implementing rotation and scaling.
The source code in THINK Pascal format is fully documented in a 78 page spiral
bound book. Between the comments in the source code and the manual an experienced
programmer should have no problem understanding how MacWireFrame is put together.
However, some of the routines may require some understanding of matrix mathematics.
It isn’t necessary to have a full understanding of all of the math though. The manual
illustrates this with the following story:
“Recently I picked up an article in a magazine which used the phrase, “matrix
multiplication is well understood”, and maybe this is the case if you’re a Ph.D.
physicist like my friend Dave, but most people like my punk rocker friend Dusty don’t
really understand it too well.”
“Punk rockers in Sacramento have this drinking game called quarters. What you
do is take a glass and put it in the middle of the table. Everyone sits around the table.
Going around in a circle each player tries to bounce the quarter off the table and up into
the glass. If you make it you get to pick one of the other players and they have to drink.
If you miss, it’s the next player’s turn unless you want to chance it, but if you miss
then you have to drink.”
“There is one other rule in the punk rock Sacramento version of quarters. If you
get really lucky and make it three times in a row you get to make up a new rule. One
time Dusty made up a this rule that before you drink you have to grab your left ear
with your right hand and yank it three times and as you yank it say arf, arf, arf. But if
you forget to do this you have to drink again. Since the winner of the game is the one left
standing when everyone else has passed out, and as the game progresses people get more
and more likely to forget the rules, this can be really strategic.”
“Once I tried to explain matrix multiplication to Dusty, how you first multiply
this row by this column and so on. “But, why do you do it that way? Why not multiply
that row and this column?”, Dusty asked. I explained to Dusty it’s just a rule that
somebody made up that proved to be useful. “Oh, I get it, this is some rule that some old
19th century mathematician made up.”, Dusty said. Making up strange rules was
something that for Dusty was well understood.”
“Too bad Dusty hadn’t lived in the 19th century or he could have been a great
mathematician. On the other hand it’s kind of sad that Sir William Rowan Hamilton
didn’t live in our time. While matrix multiplication would have already have been
thought of, he probably would have been great at the game of quarters.”
You can see from these stories that the manual tries to make the subject of
wireframes interesting, not just dry technical reading. The first half of the book tells
users how to make use of the MacWireFrame application. The last half describes the
UNIT modules used and each procedure and function is described. You’ll need to become
familiar with each function and procedure if you intend to use the MacWireFrame
source code to create your own customized wireframe application.
Each UNIT module is described first with an overall description, then with a
description of routines. Next all of the variables used. The only improvement that
could be made here would be to describe the function of each variable in more detail.
Also, there is no index to the manual. Since each module is described, it is easy to get
familiar with all of MacWireFrame’s procedures and functions.
Amplified Intelligence is now offering a special price of $299 if you order
through MacTutor. Any of you that are interested in 3D graphics will find
MacWireFrame useful.
MacWireFrame is available from:
MACTUTOR or
Amplified Intelligence
2810 Redding Ave.
P. O. Box 189279
Sacramento, CA. 95818
Phone: 916-737-1550
Price: $299 for a limited time only; List Price: $495
Requires: Macintosh II family computer with Color Monitor, THINK Pascal 2.0
or later.
Programming ability is not required for use of the MacWireFrame Application.
Programming will be required for use of the source code. Understanding of matrix math
is helpful.
Not copy protected.
THE DESKTOP LAWYER
Lawyers are generally disliked. Most of you have seen Nolo Press’s books on
various “Do-It-Yourself” law topics. Nolo’s WillMaker lets you fill in the blanks to
complete your will in just a few minutes. The Desktop Lawyer has this same
“Do-It-Yourself” law attitude. It’s produced by The Open University and distributed
by National Media Associates.
In the Desktop Lawyer is not an application, but is a set of over 300 legal
documents in MS Word format. (The templates are available on MS/DOS disks for
WordPerfect and in ASCII files). Each template is a complete legal document that can be
customized to suit your needs. Laurence J. Pino, ESQ of the law firm of Pino & Dicks of
Orlando, Florida, produced the templates to simplify “Do-It-Yourself” law.
Developers will be e specially interested in several of the templates including:
• Partnership Agreement
• Joint Venture Agreement
• Employment Agreement
• Consulting Agreement
• Business Consultant Agreement
• Employee Confidentiality , nondisclosure and nonuse agreement
• Sales Representative Agreement (Company)
• Independent Contractor Agreement
• Computer Hardware and Software Marketing Agreement
• Product License Agreement
• Grant of right to use name
• Contract for Sale and Purchase of Business
• Master Equipment Lease
• Third Party Rental Agreement
• Articles of Incorporation
• By-Laws
• Contract for sale of personal property
The other templates include Business Sales and Closing, Investment, Real Estate,
Estate Planning, Mortgages, Wills, trusts, Collection documents, agreements, leases,
rentals, and construction. The 137 page manual includes information on where to file
documents and filing fees. In addition, there are tips and comments for each of the
documents types.
Although the templates are only available in MS Word format, you will find that
they are not difficult to customize. A new version of the Desktop Lawyer is being
released in September 1991 with a revised manual that includes instructions for each
legal document. The new manual will include information such as how to fill in each
form, the circumstances you do and don’t need an attorney, and where to find basics and
procedures in other parts of the manual for making the transaction legal. Four new
forms are also being added.
There is really no other package with as many law forms in one package. People
that have used the Desktop Lawyer have said that they have “saved several times the
cost of the material”. It has something for every business owner.
The Desktop Lawyer is distributed by:
U. S. Software Resource of
Novato, CA. and Houston, TX.
8 Digital Drive, Suite 100
Novato, CA. 94949
Phone: 800-879-7899
Price: $139;
Special Introductory price $99.95 (till Dec. 31st, 1991)
The Desktop Lawyer is published by:
The Legal Institute of America for
The Open University
P. O. Box 1511
Orlando, Florida 32802
1-800-874-0388
Not copy protected.