[PPT] - CS 6958 LECTURE 8 TRIANGLES, BVH February 3, 2014 Last Time 2 PowerPoint Presentation

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CS 6958 LECTURE 8 TRIANGLES, BVH

February 3, 2014

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Last Time

 derived ray-triangle intersection  clarification:

 ray tracing inherently abstract in terms of object

specification

 we can use any object once we define an

algorithm for intersecting it with a ray (and computing localized normal direction)

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Ray Tracing Algorithm

foreach frame foreach pixel foreach sample generate ray intersect ray with objects shade intersection point

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Ray Tracing Algorithm

foreach frame foreach pixel foreach sample generate ray intersect ray with objects shade intersection point

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foreach object t_new = object.intersect(ray) t_closest = min(t_closest, t_new)

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Ray Tracing Algorithm

/// Abstract Primitive class defining properties which are required for our ray tracer. /// For now, it specifies just ray-object intersection routine, but can be extended to /// support shadow rays, bounding volumes, etc class Primitive { public: virtual bool Intersect(const Ray &ray) const = 0; } /// Sphere primitive class Sphere : public Primitive { bool Intersect(const Ray &ray) const; } // Triangle primitive class Triangle : public Primitive { bool Intersect(const Ray &ray) const; }

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Ray Tracing Algorithm

/// Abstract Primitive class defining properties which are required for our ray tracer. /// For now, it specifies just ray-object intersection routine, but can be extended to /// support shadow rays, bounding volumes, etc class Primitive { public: virtual bool Intersect(const Ray &ray) const = 0; } /// Sphere primitive class Sphere : public Primitive { bool Intersect(const Ray &ray) const; } // Triangle primitive class Triangle : public Primitive { bool Intersect(const Ray &ray) const; }

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Others:

Torus
Cone / Cylinder
Box / Rectangle
Extrusions
Surfaces of revolution
Metaballs
Iso-surface
Spline surfaces
Subdivision surfaces

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Others:

Torus
Cone / Cylinder
Box / Rectangle
Extrusions
Surfaces of revolution
Metaballs
Iso-surface
Spline surfaces
Subdivision surfaces

Ray Tracing Algorithm

/// Abstract Primitive class defining properties which are required for our ray tracer. /// For now, it specifies just ray-object intersection routine, but can be extended to /// support shadow rays, bounding volumes, etc class Primitive { public: virtual bool Intersect(const Ray &ray) const = 0; } /// Sphere primitive class Sphere : public Primitive { bool Intersect(const Ray &ray) const; } // Triangle primitive class Triangle : public Primitive { bool Intersect(const Ray &ray) const; }

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Note! We can’t use inheritance, hence we are restricted to a single primitive

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Making Ray Tracing Faster

 faster rays

 packets (less overhead per ray, cache coherence)  CPU optimizations

 fewer rays

 adaptive super-sampling (less samples)

 faster ray-primitive intersection tests  fewer ray-primitive intersection tests

 acceleration structures

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Which Operation Most Costly?

foreach frame foreach pixel foreach sample generate ray intersect ray with objects shade intersection point

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Acceleration Structures

foreach frame foreach pixel foreach sample generate ray traverse ray through acceleration structure shade intersection point

 change O(n) to O(log n), n – objects in scene  intersecting ray with structure primitive must

be cheap

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Acceleration Structures

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Acceleration Structures

 Grid

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Acceleration Structures

 Grid  Octree

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Acceleration Structures

 Grid  Octree

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)  BSP tree (Binary Space Partitioning)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)  BSP tree (Binary Space Partitioning)  BVH (Boundary Volume Hierarchy)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)  BSP tree (Binary Space Partitioning)  BVH (Boundary Volume Hierarchy)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)  BSP tree (Binary Space Partitioning)  BVH (Boundary Volume Hierarchy)

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Acceleration Structures

 Grid  Octree  KD tree (K-dimensional)  BSP tree (Binary Space Partitioning)  BVH (Boundary Volume Hierarchy)

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Idea

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BVH Traversal - Pseudocode

 description is recursive, but

TPs have small stack memory, so manage it

urselves

code will run faster

int stack[32]; // holds node IDs to traverse int sp = 0; // stack pointer into the above

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BVH Traversal - Pseudocode

current_node = root while(true) { if( ray intersects current_node ) { if( current_node._is_interior() ) { stack._push( current_node._right_child_id() ) current_node = current_node._left_child_id() continue } else intersect all triangles in leaf } if( stack._is_empty() ) break current_node = stack._pop() }

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BVH Traversal - Optimizations

 traverse closer child first  don’t traverse subtree if closer hit found

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Axis Aligned Bounding Box

 Let’s try to derive an intersection test  Box representation?

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End

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