written 8.3 years ago by | • modified 8.3 years ago |
Mumbai university > Comp > SEM 4 > Computer Graphics
Marks: 10M
Year: May 2014
written 8.3 years ago by | • modified 8.3 years ago |
Mumbai university > Comp > SEM 4 > Computer Graphics
Marks: 10M
Year: May 2014
written 8.3 years ago by |
B-Rep:
B-Rep stands for Boundary Representation.
It is an extension to the wireframe model.
B-Rep describes the solid in terms of its surface boundaries: Vertices, edges and faces as shown in figure 35
It is a method for representing shapes using the limits.
A solid is represented as a collection of connected surface elements, the boundary between solid and non-solid.
There are 2 types of information in a B – rep topological and geometric.
Topological information provides the relationships among vertices, edges and faces similar to that used in a wireframe model.
In addition to connectivity, topological information also includes orientation of edges and faces.
Geometric information is usually equations of the edges and faces.
The B-rep of 2 manifolds that have faces with holes satisfies the generalized Euler’s formula:
$$V – E + F – H = 2 (C - G)$$
Where, V = Number of vertices.
E = Number of edges.
F = Number of faces.
H = Number of holes in the faces.
C is the number of separate components (parts).
G is the genus (for a torus G = 1)
Sweep Representations:
Sweep representations are used to construct 3D object from 2D shape that have some kind of symmetry.
For example, a prism can be generated using a translational sweep and rotational sweeps can be used to create curved surfaces like an ellipsoid or a torus.
In both cases, you start with a cross-section and generate more vertices by applying the appropriate transformation.
More complex objects can be formed by using more complex transformations. Also, we can define a path for a sweep that allows you to create more interesting shapes.
CSG:
CSG stands for Constructive Solid Geometry.
It is based on set of 3D solid primitives and regularized set theoretic operations.
Traditional primitives are: Block, cones, sphere, cylinder and torus.
Operations: union, intersection, difference + translation and rotation.
A complex solid is represented using with a binary tree usually called as CSG tree.
CSG tree is shown below in figure 37.
Ray casting is a method used for determining boundaries of the resulting object if you start with a boundary representation.
Octree representations are designed to make this process easier.
Example:
Figure 38 (b) is the intersection of original solid.
Figure 38 (c) is the difference between 2 original solid.