computer graphics 2 lecture x: acceleration techniques for ray-tracing benjamin mora 1 university of...

Computer Graphics 2Lecture x:

Acceleration Techniques for Ray-Tracing

Benjamin Mora 1University of Wales

Swansea

Dr. Benjamin Mora

Introduction

2Benjamin MoraUniversity of Wales

Swansea

• Why do we need to accelerate Computer Graphics?– Because scenes are more and more complex.– Because we want interactive (~5 fps) or real-time

techniques (>30 fps).– Because global illumination algorithms takes hours to

render a single image.– Because the naïve algorithms are inefficient (and not just

a little).– Because rendering times are proportional to the

computational power, which is proportional to the money you invest and CO2 emissions…

Content


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• Ray-Tracing Oriented Techniques.– Simple Bounding Boxes (or volumes).– Grids.– Spatial Subdivisions.

• BSP and K-d Trees.• Bounded Volume Hierarchies.• Octrees.• Hierarchical Grids.

– Packed Ray-Tracing.– Multi-Level Ray-Tracing.

Ray-Tracing Oriented Techniques.


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Ray-Tracing Oriented Techniques.


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• A naïve Ray-Tracer is very inefficient.– Every ray makes an intersection test with all the

n primitives in the scene. (Complexity O(n) per ray).

– An O(log(n)) complexity per ray can be achieved on average with better techniques.

• Most acceleration techniques in Ray-Tracing use the concept of bounding boxes that are going to group a spatial subset of primitives.

Bounding Boxes


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• Example:

Naïve algorithm: 12 intersections to be tested to find the closet intersection.

Using a Bounding Box for this case: 2 Bounding box intersections at most must be done first+ 6 regular intersections. Because the ray do not intersect the second BB, there is no need to test the inner primitives.

(1)

(2)

Can this optimization also be used in case 2, since the 2 bounding boxes are intersected?

Yes, if bounding boxes tests are run in a visibility order!

Bounding Boxes


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• Bounding boxes are a very basic data structure for Ray-Tracing acceleration.

• BBs may be:– a sphere (easier to compute).– A cube.– A polyhedra.– …

• Creating the bounding box (i.e. classifying the primitives) must be done in an intelligent way…

Bounding Boxes


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• Basic algorithm for every ray:For every bounding box BB:

if BB is in front of an already detected intersection and BB is intersected by the ray then

test the intersection with all the primitives inside BB.

• Improvement can be done by testing all the bounding boxes in a Front-to-back order.

• Another improvement can be to create a hierarchy of BBs.– Similar to spatial subdivisions techniques.

Grids


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• The 3D space is subdivided with a grid.

• Every cell contains a list of primitives. – Front-to-back traversal inside a grid is easy.

• 3D-DDA traversal (See next lectures).

– Creating the grid is easier as well (do not need heuristics, unlike BBs).

– Average complexity:O(n^1/3).

BSP and Kd-Tree Demo


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Spatial Subdivision Techniques: BSP Trees


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• The 3D space is now hierarchically subdivided according a subdividing plane.

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• Ray traversal:

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• Example:



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• Recursive Ray traversal (pseudo-code):int isIntersection (node n, ray r) {

int result;

if n is a leaf node

return isThereAnIntersection(n.primitives, r);

else {

sortVisibility(n.child1, n.child2, r);

if isIntersection(n.child1, r)

result=isIntersection(n.child1, r);

if result==1 return 1;

if isIntersection(n.child2, r)

result=isIntersection(n.child2, r);

return result;

}

Spatial Subdivision Techniques: BSP-Trees


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• Binary Space Partitioning Trees.

• Logarithmic rendering complexity on average.

• Quite hard to find the best heuristic for subdivision.

• Each node represents a volumetric region delimited by convex polyhedron.

Spatial Subdivision Techniques: Kd-Trees


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• Axis-aligned BSP tree.

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• Example:



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• BSP Trees that are restricted to axis-aligned space subdivision.– Same properties as BSP trees.

• Simplify intersection computations a lot.• Memory space can be reduced as well.

– Only need to store a pointer to the 2 children, the subdivided axis(3 bits) and the location where the subdivision occurs (1 value).

• Each node represent a volumetric region delimited by a rectangular hexahedron.

• Very much used in computer graphics.



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• Heuristics to compute the tree (According Gordon Stoll, Intel, Course 41, Siggraph 2005).

• Not very efficients:– Split axis: Largest Extent.– Split Location: Middle of the extent, Centre of gravity of the

geometry.– Termination: A given number of primitives, limited depth.

• Better:– Isolate empty regions of the volume.– Termination :small cell size.– Several time faster.



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• Surface Area Heuristic. – Finding the correct splitting position.– Recursive algorithm.

• Investigate all the vertices in the node and choose the one minimizing the cost:

Cost = NodeTraversalCost +TriangleRayIntersectionCost/SA(ParentNode)*(SA(leftNode) leftTriangles+SA(rightNode)*rightTriangles)



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• SAH Example

Bounding Volume Hierarchies


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Bounding Volume Hierarchies


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• A hierarchy of bounding boxes.– MinMax of a set of triangles on x,y, and z

coordinates.

• Triangles in the set are fully included in the bounding box of a specific region.

• Easier to compute than KD-trees and Octrees.– But are often less efficient than octrees and Kd-

Trees at rendering the scene.– Often needs tp carry on traversing, even if an

intersection has been detected.

Spatial Subdivision Techniques: Octrees


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• An octree is a 3D recursive subdivision of space. Every non-leaf node has 8 children.

• Usually, the subdivision is centered on the middle of the node.

• May not be as flexible as Kd-Trees.– Small non-empty regions may create

“deeper” hierarchy/trees.

• Useful in volume rendering. – Min-max information stored instead

of empty/non-empty information. http://hpcc.engin.umich.edu/CFD/users/charlton/Thesis/html/img148.gif

Spatial Subdivision Techniques: Octrees


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Considerations on Tree Traversals


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• All spatial subdivisions work in a similar way to accelerate ray-tracing.

• A recursive top-down traversal of the tree is done.– Starting from the root node.– If node is empty=>Do nothing and Return.– If Leaf Node=>Test for an intersection with the primitives

stored inside this node. If an intersection occurs, stop recursion and return the result.

– Otherwise, find out the children of the current node that are intersected by the ray, sort them in a visibility order, and call again the function with these nodes.

Special case: Octrees


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Special case: Octrees


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• A ray can intersect between two and four of the eight possible children.

• Octree node visibility order (Painter’s algorithm, 2D example!)

• 2 and 3 can be swapped!

Viewpoint 1 23 4

2 41 3

Viewpoint

Spatial Subdivision Techniques: Hierarchical Grids


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• Similar to octrees, but the node is now grid-subdivided.

• Subdivision can be:– Regular.– Adaptive.

• Not so much used!

Packet Ray-Tracing


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• Also called coherent ray-tracing.• Reasons:

– Taking advantage of new processors:• SIMD Architectures: Single instructions applied 4 times.

– Often 3x speed-up

• Cell processor: 8 cores with SIMD capabilities.• Intersection test performed on 4 rays instead of one.

– Taking advantage of spatial coherence.• Neighbor rays will similarly traverse the acceleration structure.• A lot of traversal steps can be avoided.

• From 2x2 to 16x16 ray packets.

Multi-Level Ray-Tracing


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• Multi-level ray tracing algorithmAlexander Reshetov, Alexei Soupikov and Jim Hurley. Siggraph 2005 (ACM Transactions on Graphics), pp 1176-1185.

• Go a step further to improve the tree traversal.

• Tries to find the entry point in the tree for an as large as possible packet of rays.

• See paper for more information!



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Future of Ray-Tracing


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• Games?– Some people do believe so…– Hard to maintain acceleration structures on dynamic

scenes.

• High quality rendering.– Certainly.– Movies.– Global illumination algorithms.– Etc…

computer graphics 2 lecture x: acceleration techniques for ray-tracing benjamin mora 1 university of...

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