DMET501 Cheat Sheet

Easy to construct, modify, clip and transform. Best choice for previewing models since less inform­ation processes faster.
Could be ambiguous sometimes and could result in different interp­ret­ations. Sometimes, using wireframes might result in unreal­istic models.

A binary space partit­ioning (BSP) tree splits the space by surfaces of the solid being repres­ented (i.e., as the dividing planes). A dividing plane splits the space into two sub-spaces repres­enting two children; in front and in back of this plane (deter­mined by the normal to the plane). The process is repeated recurs­ively for each sub-space. It stops when the sub-space is entirely “in” or “out” the solid.

Used to avoid the source of ambiguity arising in wireframe. For each edge we need the following info: Vertices of this edge. Its left and right faces. The predec­essor and successor of this edge when traversing its left face. The predec­essor and successor of this edge when traversing its right face. Two more tables: The vertex table contains one entry for each vertex that represents an edge passing through it. The face table contains one entry for each face that represents one of its edges.

COP@Or­igin, z=d
COP@[0­,0,-d], z = 0
The view plane intersects the z -axis. The normal to the view plane is parallel to the z -axis. Two components of the view plane normal n are zeros. Lines parallel to the view plane will be orthog­rap­hically projected as a multi-view projec­tion. Lines parallel to the 3 rd axis (which is parallel to the view plane
normal) converge to a single vanishing point.

xyz

When the center of projection is at the origin and the normal to the view plane makes an angle θ with the yz-plane: the overall two-point perspe­ctive projection process can be achieved in three steps.
1. Rotate through an angle −θ about the y -axis so that the normal to the view plane coincides with the z -axis. 2. Perform a one-point perspe­ctive projec­tion. 3. Rotate back through an angle θ about the y -axis.

A group of adjacent faces comprises what is called a polygonal mesh.

3D Reflection xy-plane: 3D scaling (1,1,-1) yz: (-1,1,1) xz: (1,-1,1)

1. Rotate through an angle −θ about the y -axis. 2. Rotate through an angle φ about the x -axis. 3. Use the front view projection matrix

When the center of projection is at the origin and the normal to the view plane
makes an angle θ with the yz-plane and an angle φ with the zx -plane, the overall three-­point perspe­ctive projection process can be achieved in three steps. 1. Rotate through an angle φ about the x -axis so that the normal to the view plane coincides with the zx -plane. 2. Perform a two-point perspe­ctive projec­tion. 3. Rotate back through an angle −φ about the x -axis.