02-06-2012, 11:38 AM
Theory of Polygon Modeling
[attachment=23955]
In real life, objects are made of unimaginable numbers of atoms. Computers can’t quite deal with such
complex systems, so we need to use something simpler.
The simplest thing we can define on a computer is a point in space. (Similarly, if I had a piece of paper in
front of me, the easiest thing I could draw on it would be a point, I’d just tap my pencil to the paper.) A point
in space is called a vertex (“vert” for short). Several points are called vertices (“verts for short”).
Coordinates are common attributes for a vertex. Coordinates are numbers which represent its position or
point in space.
Triangles: The simplest Surface
Triangles are the simplest surface for computers to deal with, they have several properties which makes this
possible:
• They are made of straight angles. Triangles are made of straight sides and have no curves. Computer
deal with straight lines well. They do not deal with curved lines easily. Think of it this way. If I gave
you a piece of paper with two points on it and told you to draw a straight line between those two
points - you’d know exactly what I meant. Everyone I gave that paper to would draw the same line if
they followed the directions. Now suppose I gave you that same piece of paper and told you to draw a
curved, rounded line between the two points. Those are vague directions. You would be unsure of
what exactly I wanted you to draw. Each person I gave that assignment to would draw slightly
different curved lines. In order to make sure everyone drew identical curves between the two points I
would need to give much more complicated directions.
• They are flat.
• They cannot self intersect. Computers have a hard time handling intersections. So triangles are easier
to deal with because it is impossible for them to go through themselves.
*Screen shot of simple med to complicated models made of triangles
In the examples below, using 3D Studio Max and Maya, I've made two triangles and pulled the center
connecting edge upwards dividing the flat, or “planar” surface.
Polygons: The Next Simplest Surface.
A polygon is like a triangle but has more sides. A square is a polygon. Any polygon can easily be broken down
into triangles, so it is still quite simple. Polygons are usually flat, or close to being flat. If the two triangles
form an extreme angle (are not flat) then we usually won’t call them a polygon.
Concept of Normals
Each triangle or polygon in 3D software has a “normal”. If a polygon was perfectly flat, its normal would point
straight up, away from the surface, always perpendicular. In order to simplify the amount of work the
computer needs to do, 3D software can perform something called “backface culling”. Cull meaning “to not
show”, “trim away”, or “ignore” and backface means the back of faces or the back of polygons. "Backface
culling" means not showing the back of polygons, only showing the front, or more accurately, the side the
normal points from.
[attachment=23955]
In real life, objects are made of unimaginable numbers of atoms. Computers can’t quite deal with such
complex systems, so we need to use something simpler.
The simplest thing we can define on a computer is a point in space. (Similarly, if I had a piece of paper in
front of me, the easiest thing I could draw on it would be a point, I’d just tap my pencil to the paper.) A point
in space is called a vertex (“vert” for short). Several points are called vertices (“verts for short”).
Coordinates are common attributes for a vertex. Coordinates are numbers which represent its position or
point in space.
Triangles: The simplest Surface
Triangles are the simplest surface for computers to deal with, they have several properties which makes this
possible:
• They are made of straight angles. Triangles are made of straight sides and have no curves. Computer
deal with straight lines well. They do not deal with curved lines easily. Think of it this way. If I gave
you a piece of paper with two points on it and told you to draw a straight line between those two
points - you’d know exactly what I meant. Everyone I gave that paper to would draw the same line if
they followed the directions. Now suppose I gave you that same piece of paper and told you to draw a
curved, rounded line between the two points. Those are vague directions. You would be unsure of
what exactly I wanted you to draw. Each person I gave that assignment to would draw slightly
different curved lines. In order to make sure everyone drew identical curves between the two points I
would need to give much more complicated directions.
• They are flat.
• They cannot self intersect. Computers have a hard time handling intersections. So triangles are easier
to deal with because it is impossible for them to go through themselves.
*Screen shot of simple med to complicated models made of triangles
In the examples below, using 3D Studio Max and Maya, I've made two triangles and pulled the center
connecting edge upwards dividing the flat, or “planar” surface.
Polygons: The Next Simplest Surface.
A polygon is like a triangle but has more sides. A square is a polygon. Any polygon can easily be broken down
into triangles, so it is still quite simple. Polygons are usually flat, or close to being flat. If the two triangles
form an extreme angle (are not flat) then we usually won’t call them a polygon.
Concept of Normals
Each triangle or polygon in 3D software has a “normal”. If a polygon was perfectly flat, its normal would point
straight up, away from the surface, always perpendicular. In order to simplify the amount of work the
computer needs to do, 3D software can perform something called “backface culling”. Cull meaning “to not
show”, “trim away”, or “ignore” and backface means the back of faces or the back of polygons. "Backface
culling" means not showing the back of polygons, only showing the front, or more accurately, the side the
normal points from.