Search results
Results from the WOW.Com Content Network
Each pair of parallel planes defines a slab, and the volume contained in the box is the intersection of the three slabs. Therefore, the portion of ray within the box (if any, given that the ray effectively intersects the box) will be given by the intersection of the portions of ray within each of the three slabs. [3]
The Möller–Trumbore ray-triangle intersection algorithm, named after its inventors Tomas Möller and Ben Trumbore, is a fast method for calculating the intersection of a ray and a triangle in three dimensions without needing precomputation of the plane equation of the plane containing the triangle. [1]
CSG objects can be represented by binary trees, where leaves represent primitives, and nodes represent operations. In this figure, the nodes are labeled ∩ for intersection, ∪ for union, and — for difference. Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling.
Differential cone-tracing, considering a differential angular neighborhood around a ray, avoids the complexity of exact geometry intersection but requires a LOD representation of the geometry and appearance of the objects. MIPmapping is an approximation of it limited to the integration of the surface texture within a cone footprint.
Most implementations of the ray casting algorithm consecutively check intersections of a ray with all sides of the polygon in turn. In this case the following problem must be addressed. If the ray passes exactly through a vertex of a polygon, then it will intersect 2 segments at their endpoints. While it is OK for the case of the topmost vertex ...
A k-DOP is the Boolean intersection of extents along k directions. Thus, a k-DOP is the Boolean intersection of k bounding slabs and is a convex polytope containing the object (in 2-D a polygon; in 3-D a polyhedron). A 2-D rectangle is a special case of a 2-DOP, and a 3-D box is a special case of a 3-DOP.
Take the intersection point C of the ray OA with the circle P. Connect the point C with an arbitrary point B on the circle P (different from C and from the point on P antipodal to C) Let h be the reflection of ray BA in line BC. Then h cuts ray OC in a point A '. A ' is the inverse point of A with respect to circle P. [4]: § 3.2
No intersection at all; Intersection in exactly one point; Intersection in two points. Methods for distinguishing these cases, and determining the coordinates for the points in the latter cases, are useful in a number of circumstances. For example, it is a common calculation to perform during ray tracing. [1]