Constructive Solid Geometry Ray Tracing CSG Models

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Presentation transcript:

Constructive Solid Geometry Ray Tracing CSG Models CSE 681

CSG Form object as booleans of primitive objects Primitives: sphere, cube, cylinder, cone Boolean operators: union, intersection, difference Tree structure used to manage operations Leaf nodes are primitive objects Intermediate nodes specify combination operator CSE 681

Union B C + C B Ray intersects union: at first intersection Min (tCmin, tBmin ) CSE 681

Possible ways for 2 spans to overlap CSE 681

Intersection B C ++ C B First time in B and in C If ((tCmin< tBmin ) and (tCmax> tBmin ) ): tBmin Else If ((tBmin< tCmin ) and (tBmax> tCmin ) ): tCmin Else: none CSE 681

Difference B C -+ C B If ((tBmin< tCmin ): tBmin Else if (tCmax< tBmax ): tCmax Else: none First time in B not in C CSE 681

Difference B +- C C B First time in C not in B If ((tCmin< tBmin): tCmin Else if (tBmax< tCmax ): tBmax Else: none CSE 681

Primitives Anything that can be intersected (easily) with a ray Conics: solve analytically using R(t) Convex polyhedra A plane (a cutting plane is useful) can be used as a modeling tool (boolean operations) surface model (e.g., polyhedron) computed from CGS or Can be used as a model representation keep tree structure and ray trace directly CSE 681

Controlling the Combinations + - + ? CSE 681

Tree Structure - - + T5 + + T4 + T3 T2 T1 rectangle rectangle circle CSE 681

Tree Structure #1 CSE 681

Tree Structure + - + T5 + + T4 - T3 T2 T1 rectangle rectangle circle CSE 681

Tree Structure #2 CSE 681

Tree Structure Intersect ray with leaf nodes (primitive objects) Combine intersection spans according to intermediate nodes union intersection difference Might create multiple spans CSE 681

Union of Spans CSE 681

Intersection of Spans CSE 681

Difference of Spans CSE 681

Normals of CSG intersections Normal of some surface (or its negation) Union or intersection: positive normal of intersected surface CSE 681

Difference normals Intersection is one of: tmin of positive object – normal of surface tmax of negative object – negated normal CSE 681

Add transformations to tree http://www.cs.mtu.edu/~shene/COURSES/cs3621/NOTES/model/csg.html CSE 681

Bounding Volumes - Construction Use bounding volumes at leaf nodes Union bounding volumes at interior nodes circle rectangle + - T1 T2 T3 T4 T5 Traversal Top-down Test bounding volume at interior CSE 681

Examples CSE 681

Examples CSE 681

Examples CSE 681