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Angle between ray and triangle mesh

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Are there any algorithms to quickly compute the angle between a ray and a large triangle mesh? (Or, at the minimum, whether the angle is less than some fixed threshold.)

By angle from a ray I mean the smallest angle $theta$ such that a cone of half-angle $theta$ whose vertex is the vertex of the ray and whose axis is aligned with the ray will intersect the mesh. The mesh is a set of arbitrary triangles in 3d space.

For the related problems of finding the distance from a point or whether or not a ray intersects there are fast algorithms using axis-aligned bounding box trees (e.g. CGAL's AABB tree implementation). However, I haven't been able to find any information about find the angle from a ray.

Note: I need to make many queries with different rays against a given mesh, so an algorithm that necessitates precomputation with the mesh (like constructing an AABB tree or octree) is ok. The number of triangles in the mesh and the number of queries (rays) may both be as large as 10 million.

geometry computational-mathematics computational-geometry

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asked Mar 15 at 16:20

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0

$begingroup$

Are there any algorithms to quickly compute the angle between a ray and a large triangle mesh? (Or, at the minimum, whether the angle is less than some fixed threshold.)

By angle from a ray I mean the smallest angle $theta$ such that a cone of half-angle $theta$ whose vertex is the vertex of the ray and whose axis is aligned with the ray will intersect the mesh. The mesh is a set of arbitrary triangles in 3d space.

For the related problems of finding the distance from a point or whether or not a ray intersects there are fast algorithms using axis-aligned bounding box trees (e.g. CGAL's AABB tree implementation). However, I haven't been able to find any information about find the angle from a ray.

Note: I need to make many queries with different rays against a given mesh, so an algorithm that necessitates precomputation with the mesh (like constructing an AABB tree or octree) is ok. The number of triangles in the mesh and the number of queries (rays) may both be as large as 10 million.

geometry computational-mathematics computational-geometry

share|cite|improve this question

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312

$endgroup$

add a comment | 

$begingroup$

Are there any algorithms to quickly compute the angle between a ray and a large triangle mesh? (Or, at the minimum, whether the angle is less than some fixed threshold.)

By angle from a ray I mean the smallest angle $theta$ such that a cone of half-angle $theta$ whose vertex is the vertex of the ray and whose axis is aligned with the ray will intersect the mesh. The mesh is a set of arbitrary triangles in 3d space.

For the related problems of finding the distance from a point or whether or not a ray intersects there are fast algorithms using axis-aligned bounding box trees (e.g. CGAL's AABB tree implementation). However, I haven't been able to find any information about find the angle from a ray.

Note: I need to make many queries with different rays against a given mesh, so an algorithm that necessitates precomputation with the mesh (like constructing an AABB tree or octree) is ok. The number of triangles in the mesh and the number of queries (rays) may both be as large as 10 million.

geometry computational-mathematics computational-geometry

share|cite|improve this question

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312

$endgroup$

share|cite|improve this question

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312

share|cite|improve this question

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312

asked Mar 15 at 16:20

2012rcampion2012rcampion

460312