In order to do this week's homework (due Tuesday Oct 3), the following notes from class should be useful.
NOTES ON REPRESENTING 3D SHAPES WITH POLYGONS
A shape can be represented as an object that contains:
If we let angle theta take on each of the N values around a circle:
θ = 2π i / N , where i = 0, 1, 2, .... N-1then we can create the central tube with 2N vertices (each with x,y,z and normal nx,ny,nz), where the first N vertices are:
[cosθ, sinθ, -1, cosθ, sinθ, 0]and the last N vertices are:
[cosθ, sinθ, +1, cosθ, sinθ, 0]Each of the faces of this central tube will have four sides, so the
facearray needs to consist of:
The front cap will contain N+1 vertices, including the added central point [0,0,1, 0,0,1], and its faces will consist of N triangles. The back cap will also contain N+1 vertices, including the added central point [0,0,-1, 0,0,-1], and its faces will also consist of N triangles. I leave it as an exercise for you to create these two end caps. When you've built the complete cylinder, you should have 4N+2 vertices and 3N faces.
0 1 N+1 N 1 2 N+2 N+1 ... ... ... ... N-2 N-1 2N-1 2N-2 N-1 0 N 2N-1
Because we need to separately store vertices that have different normals, there will be 24 vertices; one for each corner of each face of the cube. For example, the cube's four vertices on its leftmost face (the face that points into negative x), are:
Notice that I have ordered these four vertices in counterclockwise order, if you are looking at this face of the cube from the outside. I leave it to you to create the vertices for the other five faces of the cube.
-1 -1 -1 -1 0 0 -1 -1 +1 -1 0 0 -1 +1 +1 -1 0 0 -1 +1 -1 -1 0 0
The face data for the cube is rather simple, as we discussed in class:
TRANSFORMING AND RENDERING SHAPES
0 1 2 3 4 5 6 7 ... ... ... ... 20 21 22 23
At every animation frame, for each shape in your scene you'll want to:
drawLinebetween the projection onto the image of successive vertices in that face, as we discussed in class.
I recommend that in your Shape object
you maintain an array
into which you
can place your transformed vertex data every frame
between steps (2) and (3) above.
WINDOW AND VIEWPORT
In order to properly project each transformed vertex onto your image, so that you can draw lines between them, you'll need to do a window transform followed by a viewport transform.
The window transformation places an object floating in 3D space into position in front of the virtual "camera". For now, you can just use a really trivial window transformation:
[x,y,z] → [x,y]Later on we will do more interesting things, like perspective and animating cameras. The viewport transformation maps the coordinates (x,y) into some pixel coordinates (px, py). For now you can just use the simple viewport transform:
[x,y] → [ (int)(W/2 + x*W/2) , (int)(H/2 - y*W/2) ]where W and H are the width and height of your applet, in pixels.