Manual-Geometry.md

Klamp't Manual: Geometry and Appearance

• Geometries and collision geometries
  • Geometric representations
  • Geometric operation support
  • API summary
  • Geometry caching
• Appearance

Klamp't uses a variety of geometry types to define geometric primitives, triangulated meshes, and point clouds. Each geometry may also be associated with an Appearance.

Geometries and collision geometries

Klamp't stores Geometry datain an object's local frame.

The notion of a collision geometry combines some underlying geometric data with transformations and collision acceleration structures. Collision geometries have a current transformation that sets where they exist in space, and is used for collision testing. Collision geometries also support an additional, nonnegative margin setting that "expands" the underlying geometry when performing collision testing. The margin does not actually affect the geometric data, but rather it changes the distance threshold that is used to consider colliding vs. noncolliding geometries.

Geometric representations

The following geometric representations are currently supported:

• Geometric primitive (Primitive): axis-aligned boxes, oriented boxes, lines, rays, segments, triangles, planar polygons, spheres, ellipsoids, and planar circles.
• Convex polytope (ConvexHull): A convex hull of a set of points.
• Triangle mesh (TriangleMesh): the most common geometry representation used in video games and CAD models. Can also contain appearance data.
• Point cloud (PointCloud): most commonly used in laser scanners and RGBD sensors. Can also contain color and other per-point properties. If the radius property is given, then each point is treated like a sphere.
• Implicit surface voxel grid (ImplicitSurface): a volumetric representation where values < 0 are inside, 0 is the surface, and > 0 are outside. Usually a signed distance function (SDF). Can also represent other implicit functions and TSDFs for some operations (visualization, conversion, inside-outside tests).
• Occupancy map voxel grid (OccupancyGrid): a volumetric representation where values > 0.5 (or some other value) are occupied.
• Height map / depth map (Heightmap): an elevation map or a perspective depth map. Can also contain color and other properties.

In addition, there is a notion of a geometry Group, which can combine multiple sub-geometries.

Geometric operation support

Not all representations support all operations, and some representations yield much better performance (speed and accuracy) than others. To get optimal performance from your program, you should learn which operations are suited for which representations.

To get a better sense of how operations affect the geometries, the geometrytest.py test program in Klampt-examples can be used. This allows you to convert any two geometries into any supported format and perform various queries. Use the Actions menu to convert and switch between proximity query modes. Klampt-examples and geometrytest.py on Github.

The rest of this section provides detailed information about Klampt's support for various geometry operations. (Here, 🕑 means support is on the TODO list for the near future.)

Loading / Saving

All types supported.

Triangle meshes can be saved/loaded from nearly all types (STL, OBJ, OFF, PLY, GLTF, etc), unless you are building from source and Assimp is unavailable at build time.

Point clouds can be saved/loaded from PCL format.

Primitives, convex hulls, and voxel grids use custom formats.

Heightmaps are stored in a custom JSON format. Heightmap images can be loaded from many image file formats on Windows or if ImageMagick was installed while KrisLibrary is built; otherwise, only BMP, TGA, and PPM are supported.

OpenGL drawing

Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
✔️	✔️	✔️	✔️	✔️	✔️	✔️

Type conversions

(Converting from the type listed in column to type listed in row.)

To ↓ \ From →	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP		❌	❌	❌	❌	❌	❌
CP	✔️		✔️¹	✔️	✔️	✔️	✔️
TM	✔️	✔️		❌	✔️	✔️	✔️
PC	✔️	✔️	✔️		✔️	✔️	✔️
IS	✔️	✔️	✔️	❌		❌	✔️
OG	✔️	✔️	✔️	✔️	✔️		✔️
HM	✔️	❌	✔️	✔️	✔️	✔️

1. Convex decomposition of a non-convex watertight mesh can be performed with an appropriate parameter to the convert function.

These are shown in the following image:

Note that a depth map is considered to be viewed from the "bottom up", so the occupied space is considered to be any space above the map. Here, the depth values outside of the sphere are assumed invalid.

Indirect conversions to a third type can be used to do some unsupported conversions. For example, convex polytope -> triangle mesh -> heightmap can replace the unsupported convex polytope -> heightmap conversion. Occupancy grid -> triangle mesh -> implicit surface can replace the unsupported occupancy grid -> implicit surface conversion.

Many conversions (mesh -> convex polytope, implicit surface, occupancy grid, heightmap) also depend on a resolution parameter. If the resolution is set too low, then the fidelity of the resulting geometry may suffer. As an example, the below image shows a CAD model of the Boston Dynamics Atlas torso converted to an implicit surface at two different resolutions:

If in doubt, you should visualize the result (in Python, you can simply run from klampt import vis; vis.debug(geom)).

Conversion from a group to a target type is only available when:

1. There is a single object that can be converted to the target type.
2. The target is triangle mesh or point cloud, and all objects can be converted to the target type.

We perform computation speed tests to profile the performance of geometric operations. The test set contains both simple and complex geometries and is tested on a machine with a 5.4 Ghz Intel i9 processor. Simple test geometries are approximately spherical, have unit size, and have the following complexity:

• GP: sphere
• CP: 8 vertices
• TM: 624 triangles
• PC: 761 points
• IS/OG: 64 x 64 x 64 grid
• HM: 256 x 256 grid

While complex test geometries have the following complexity:

• CP: 3,122 vertices
• TM: 70,224 triangles
• PC: 157,000 points
• IS/OG: 256 x 256 x 256 grid
• HM: 2,048 x 2,048 grid

Example conversion speeds are shown below (in ms). Algorithmic complexity is approximately linear in the number of elements for all representations except for Convex Polytope, which is superlinear. Conversions are listed from the type listed in column to type listed in row.

Simple geometries:

From → / To ↓	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive
ConvexHull	2.289		6.244	2.838	495.649	2.827	1192.522
TriangleMesh	0.011	0.044			38.945	0.173	7.988
PointCloud	0.056	0.049	0.102		7.286	0.043	3.521
ImplicitSurface	0.499	17.712	22.407				106.069
OccupancyGrid	0.569	17.732	1.508	0.038	1.025		106.331
Heightmap	5.396		4.428	0.812	12.108	0.052

Complex geometries:

From → / To ↓	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive	0.000
ConvexHull	0.072	0.002	765.821	70.139	12509.097	1614.323	3989.334
TriangleMesh	0.001	21.802	0.707		978.975	766.626	718.425
PointCloud	0.005	22.913	10.826	8.696	631.070	619.788	424.437
ImplicitSurface	0.351	236.135	14057.825		33.795		6995.770
OccupancyGrid	0.387	239.799	165.434	174.888	83.796	33.489	7010.963
Heightmap	10.661		32.363	8.649	993.740	992.110	4.293

Proximity query acceleration data structures

To accelerate proximity queries (collision, ray casting, distances, etc.), most geometries create auxiliary data structures. These are initialized when a proximity query is first called. These structures are cached as long as the collision geometry undergoes rigid transforms via SetTransform (C++) / setCurrentTransform (Python).

However, the data structures must be refreshed if the geometry data is changed. The overhead of precomputation can be small for simple geometries. However, for complex geometries, the overhead can be substantial, so it is best to avoid interleaving changes to the geometry data with proximity queries.

Geometric primitive	None
Convex polytope	SOLID3 data structure
Triangle mesh	PQP bounding volume hierarchy
Point cloud	Sparse voxel grid and octree
Implicit surface	Octree
Occupancy grid	List of occupied and surface cells
Heightmap	None

Example precomputation speeds are shown below (in ms):

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Simple	0.000	0.000	1.203	0.142	0.975	1.395	0.128
Complex	0.000	0.000	504.044	13.737	630.696	1073.331	7.041

Miscellaneous queries

Bounding box queries yield an axis-aligned (C++ and Python) or oriented bounding box (C++ only).

Ray casts find the first point of intersection between the geometry and a ray.

Support queries find the farthest point on the geometry in some direction.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Bounding box	✔️	✔️	✔️¹	✔️¹	✔️	✔️	✔️
Ray cast	✔️	❌²	✔️	✔️	✔️	✔️	✔️
Support	✔️	✔️	✔️	✔️	❌	❌	❌

1. A fast approximate method is available.
2. A limitation of SOLID3.

Point queries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Containment	✔️	✔️	✔️¹	✔️	✔️	✔️	✔️
Distance	✔️²	✔️²	✔️	✔️²	✔️²	🕑	🕑

1. uses a heuristic to determine inside/outside.
2. signed distance supported.

An example of point containment queries is shown below.

An example of a point distace query is shown below with the query asking for the distance and closest point on the red geometry to the center of the green circle.

Example computation speeds are shown below (in ms):

Simple geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Bounding box	0.000	0.001	0.000	0.000	0.001	0.001	0.000
Ray cast	0.000		0.000	0.000	0.000	0.000	0.003
Support	0.000	0.000	0.001	0.003
Pt. Containment	0.000	0.002	0.005	0.000	0.000	0.000	0.000
Pt. Distance	0.000	0.003	0.006	0.003	0.000

Complex geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Bounding box	0.001	0.003	0.001	0.000	0.001	0.001	0.001
Ray cast	0.000		0.000	0.000	0.000	0.000	0.020
Support	0.000	0.000	0.047	0.538
Pt. Containment	0.000	0.003	0.004	0.000	0.000	0.000	0.000
Pt. Distance	0.000	0.005	0.010	0.042	0.000

Collision detection

Collision detection detects whether two objects overlap. The extended version returns the element indices that overlap up to some number of max contacts, and if max contacts = 1 this costs no more time than the simple (boolean) version. Below, the orange triangles on the red object collide with the green triangles on the yellow object.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	✔️²	✔️²	✔️²	✔️²	✔️¹	✔️²	✔️³
CP	✔️²	✔️	✔️	✔️	❌	✔️³	✔️³
TM	✔️²	✔️	✔️	✔️	✔️³	✔️³	✔️³
PC	✔️	✔️	✔️	✔️	✔️	✔️³	✔️
IS	✔️¹	❌	✔️³	✔️	✔️³	✔️³	✔️³
OG	✔️²	✔️³	✔️³	✔️³	✔️³	✔️³	✔️
HM	✔️³	✔️³	✔️³	✔️	✔️³	✔️	🕑

1. for a couple geometric primitives (usually point and sphere).
2. for common geometric primitives (usually point, sphere, box, and triangle)
3. not accelerated, or scaling to large geometries is poor.

Within-distance detection is a boolearn query that detects whether two objects are within a given distance from one another. It is usually faster than distance calculation. The extended version returns the element indices that overlap up to some number of max contacts, and if the max contacts = 1 then this costs no more time than the simple (boolean) version. Below, the orange triangles on the red object are within 0.1 units from the green triangles on the yellow object.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	✔️²	✔️²	✔️²	✔️²	✔️¹	✔️²	❌
CP	✔️²	✔️	✔️	✔️	❌	✔️³	❌
TM	✔️²	✔️	✔️	✔️	✔️³	✔️³	❌
PC	✔️²	✔️	✔️	✔️	✔️	✔️³	❌
IS	✔️¹	❌	✔️³	✔️	✔️³	✔️³	❌
OG	✔️²	✔️³	✔️³	✔️³	✔️³	❌	❌
HM	❌	❌	❌	❌	❌	❌	❌

1. for a couple geometric primitives (usually point and sphere).
2. for common geometric primitives (usually point, sphere, box, and triangle)
3. not accelerated, or scaling to large geometries is poor.

Example computation speeds are shown below (in ms). Note that speeds vary significantly on the relative pose, size, and resolution of the objects, where performance worsens with close-but-not-colliding, highly overlapping, similar sized, and high-resolution objects.

Simple geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	0.000	0.003	0.001	0.014	0.001	0.007	0.011
CP	0.003	0.002	0.011	0.014		0.004	0.072
TM	0.001	0.011	0.012	0.437	0.124	0.617	0.029
PC	0.014	0.014	0.437	0.170	0.039	8.042	0.016
IS	0.001		0.124	0.039	8.439	1.314	0.499
OG	0.007	0.004	0.617	8.042	1.314	1.396	0.932
HM	0.011	0.072	0.029	0.016	0.499	0.932

Complex geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	0.001	0.007	0.002	0.313		0.005	0.001
CP	0.007	0.006	8.827	28.404		0.089	63.090
TM	0.002	8.827	0.011	2.295	4.608	31.010	0.884
PC	0.313	28.404	2.295	4.537	1.905	560.186	0.021
IS			4.608	1.905	7.504	87.130	3.685
OG	0.005	0.089	31.010	560.186	87.130	27.407	12.617
HM	0.001	63.090	0.884	0.021	3.685	12.617

Distance query

Distance queries determine the minimium distance between objects. Some geometry pairs also support signed distance queries, which return the negative penetration depth if the objects are overlapping.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	✔️²	✔️²	✔️²	✔️	✔️¹	❌	❌
CP	✔️²	✔️	❌	✔️	❌	❌	❌
TM	✔️²	❌	✔️	✔️	🕑	❌	❌
PC	✔️	✔️	✔️	✔️	✔️	❌	❌
IS	✔️¹	❌	🕑	✔️	❌	❌	❌
OG	❌	❌	❌	❌	❌	❌	❌
HM	❌	❌	❌	❌	❌	❌	❌

1. for a couple of primitives (usually point and sphere).
2. for common geometric primitives (usually point, sphere, box, and triangle)

Example computation speeds are given below (in ms):

Simple geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive	0.001	0.005	0.003	0.003	0.001
ConvexHull	0.005	0.005		0.036
TriangleMesh	0.003		0.208	0.699
PointCloud	0.003	0.036	0.699	0.165	0.047
ImplicitSurface	0.001			0.047
OccupancyGrid
Heightmap

Complex geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive		0.025	0.068	0.062
ConvexHull	0.025	0.056		0.149
TriangleMesh	0.068		0.635	13.961
PointCloud	0.062	0.149	13.961	34.039	1.883
ImplicitSurface				1.883
OccupancyGrid
Heightmap

Contact detection

Contact detection is used in physics simulation and stability prediction to produce accurate estimates of all the contact points that would be active between two objects that are touching. Below, the contact points are shown as orange points and normals are shown as red lines.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	✔️²	✔️	✔️¹	✔️	✔️²	❌	❌
CP	✔️	✔️	❌	✔️	❌	❌	❌
TM	✔️¹	❌	✔️	✔️	✔️	❌	❌
PC	✔️	✔️	✔️	✔️	✔️	❌	❌
IS	✔️²	❌	✔️	✔️	❌	❌	❌
OG	❌	❌	❌	❌	❌	❌	❌
HM	❌	❌	❌	❌	❌	❌	❌

1. Only produces a single contact point, may lead to inaccurate simulations.
2. For some primitives.

Example computation speeds are given below (in ms):

Simple geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive	0.000	0.004	0.001	0.001	0.001
ConvexHull	0.004	0.001		0.001
TriangleMesh	0.001		0.022	0.630	0.194
PointCloud	0.001	0.001	0.630	0.244	0.002
ImplicitSurface	0.001		0.194	0.002
OccupancyGrid
Heightmap

Complex geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive		0.016	0.002	0.001
ConvexHull	0.016	0.003
TriangleMesh	0.002		0.007	12.555	23.283
PointCloud	0.001		12.555	17.852	0.022
ImplicitSurface			23.283	0.022
OccupancyGrid
Heightmap

Geometric operations

Transforms here refer to transforming the underlying geometry by translation, rotation, and/or scaling. (Recall that all collision objects have a current transform which can be set with nearly zero overhead.)

Remesh operations refine the representation to a specified coarser or finer resolution.

Union operations gather multiple objects of the same type into a single object. If a union cannot be performed, then a Group geometry is produced by the union operation.

Extract ROI operations extract a region (bounding box) from the object to produce an object of the same type. The below ROI of a mesh was computed and then the original mesh was moved to the left for visualization clarity.

Slice operations take a planar slice through the object.

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Rigid transform	✔️	✔️	✔️	✔️	❌	❌	✔️
Nonuniform scale	❌	✔️	✔️	✔️	✔️	✔️	✔️
Scale + rigid transform	✔️	✔️	✔️	✔️	❌	❌	❌
Remesh	❌	❌	✔️	✔️	✔️	✔️	✔️
Union	❌	✔️	✔️	✔️	❌	❌	❌
ROI	❌	❌	✔️	✔️	✔️¹	✔️¹	✔️¹²
Slice	❌	❌	✔️	✔️	❌	❌	❌

1. Only axis-aligned.
2. Depth maps not supported.

Merge operations union a geometry into an existing representation: (merging the type listed in row into target type listed in column)

Into → / From ↓	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
GP	❌	❌	❌	❌	✔️	✔️	✔️
CP	❌	✔️	❌	❌	✔️	✔️	❌
TM	❌	❌	✔️	❌	✔️	✔️	✔️
PC	❌	❌	❌	✔️	✔️	✔️	✔️
IS	❌	❌	❌	❌	✔️	✔️	✔️
OG	❌	❌	❌	❌	❌	✔️	✔️
HM	❌	❌	❌	❌	❌	❌	✔️¹

1. domains must be aligned. Support for unaligned domains is 🕑.

For triangle mesh and point cloud targets, it is recommended that you first convert the merged geometry into the desired type before merging.

Below is an illustration of a geometric primitive (sphere) being merged into a heightmap of a lunar terrain. For visualization clarity, the primitive was moved to the right after merging.

Computation speeds are shown below (in ms):

Simple geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Transform	0.000	0.078	0.003	0.016	0.003	0.004	0.000
Remesh			0.502	0.209	0.042	6.911	0.008
Union		0.254	0.049	0.188
ROI			0.002	0.015	0.039	0.027	0.114
Slice			0.001	0.004

Merge Into → / From ↓	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive					28.071	18.002	1.405
ConvexHull		0.170			785.527	47.786
TriangleMesh			4.195		323.612	17.878	1.836
PointCloud				0.834	61.015	14.178	1.159
ImplicitSurface					17.738	23.709	12.708
OccupancyGrid						22.014	12.785
Heightmap

Complex geometries

	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Transform	0.000	72.583	0.349	3.878	14.325	0.000	2.626
Remesh			24.164	11.309	0.048	338.694	0.008
Union		133.693	5.146	42.201
ROI			0.002	2.405	0.177	0.106	5.983
Slice			0.001	0.002

Merge Into → / From ↓	Geometric primitive	Convex polytope	Triangle mesh	Point cloud	Implicit surface	Occupancy grid	Heightmap
Primitive					2725.712	1095.119	107.943
ConvexHull		133.480			83310.352	65026.609
TriangleMesh			529.401		3051.742	945.973	123.200
PointCloud				193.659	15528.338	953.143	77.381
ImplicitSurface					1095.707	1526.846	1129.939
OccupancyGrid						1443.728	1012.194
Heightmap

API summary

C++

Geometry data is stored in the AnyGeometry3D type and collision geometries are stored in the AnyCollisionGeometry3D type. These are essentially container types that abstract the underlying geometry and collision acceleration data structures. To operate on the data therein, users will need to inspect the geometry's type and cast to the appropriate type. The data contained within an AnyGeometry3D is an instance of a Geometry3D[X] object. The collision data contained within an AnyCollisionGeometry3D is stored in an instance of a Collider3D[X] object.

Detailed datatype documentation can be found in the following files:

• KrisLibrary/math3d/geometry3d.h defines 3D geometric primitives, including Point3D, Segment3D, Triangle3D, AABB3D, Box3D, Sphere3D, and Ellipsoid3D. There is also a GeometricPrimitive3D class that abstracts common operations on any geometric primitive.
• KrisLibrary/meshing/TriMesh.h defines 3D triangle meshes.
• KrisLibrary/meshing/PointCloud.h defines a 3D point cloud. Each point may contain a variety of other named properties, including color, normal, id, etc.
• KrisLibrary/meshing/Heightmap.h defines a height map or depth map (as a perspective projected height map). The map may be colored and can contain other property images.
• KrisLibrary/meshing/VolumeGrid.h defines a volumetric grid, which may contain an implicit function or occupancy map.

Geometry caching

When multiple objects load the same geometry file, Klamp't uses a caching mechanism to avoid reloading the file from disk and re-creating collision acceleration structures. This is essential for loading very large scenes with many replicated objects.

In C++, if you change the underlying geometry data in a ManagedGeometry, it will affect all other shared geometries. To avoid this effect, call ManagedGeometry.SetUnique first.

Appearance

Klampt appearances are relatively simple materials that work with OpenGL and can specify:

• Color
• Transparency
• Vertex / edge / face drawing with separate color/transparency
• Vertex / edge size
• 1D, 2D, or 3D textures
• Texture projection mapping
• Per-vertex / per-face colors
• Mesh creasing
• Silhouette drawing

Silhouette data and mesh creasing require some precomputation overhead, which can be substantial for complex geometries. To avoid incurring this overhead, turn them off.

Some geometry types (TriangleMesh, PointCloud, Heightmap) can also contain appearance data. An appearance created from these objects will load the associated apperance data upon initialization.

All geometry types except for point clouds are converted to a triangle mesh for rendering. This mesh is cached; if you change the geometry data, GeometryAppearance.Refresh() (C++) / Appearance.refresh() (Python) will need to be called. Note that this will read the geometry's appearance again. If you change the geometry data but want to keep your manually-specified changes to the appearance, you will need to call GeometryAppearance.RefreshGeometry() (C++). TODO: The Python API does not have a version of this yet.

Proper rendering of transparent objects requires some care to draw objects from back to front. The WorldModel.DrawGL() method (C++) and the Python vis module handle this automatically. Artifacts may still appear between elements within an object, which are not automatically ordered.

Known issues and plans

• GeometricPrimitive support for segments, triangles, and polygons is sparse. Not sure how much demand there is for these primitives.
• PointCloud per-point radius support is spotty and has not been tested thoroughly.
• Want to include Gaussian Splatting representations in PointCloud at some point in the future.
• TSDF proximity detection routines are largely incorrect.
• Heightmap interpolation is still unimplemented.

Visualization

• TSDFs aren't drawn correctly, showing back faces at -truncationDistance. TODO: throw out back faces.
• Fractional occupancy grids are drawn as binary. TODO: draw fractional cells transparently? Or build a higher level function.

Conversions and merging

• Heightmap -> TriangleMesh conversions does not throw out discontinuities. TODO: interpret parameter as depth threshold.
• Heightmap merging could benefit from GPU acceleration. Need to devise a coherent strategy for caching OpenGL elements with geometries.

Collisions

Availability

• ImplicitSurface - ConvexHull isn't implemented. Could iterate over cells that the ConvexHull's bounding box overlaps, or use hierarchy.
• ImplicitSurface - box isn't implemented. Could iterate over cells that the box's bounding box overlaps, or use hierarchy.

Speed

• ImplicitSurface - OccupancyGrid slow when close but not colliding
• OccupancyGrid - OccupancyGrid slow when close but not colliding
• Primitive - Heightmap is slow for perspective heightmaps when the primitive is near origin. Could benefit from GPU acceleration.
• ConvexHull - Heightmap is slow for perspective heightmaps when the convex hull is near origin. Could benefit from GPU acceleration.
• PointCloud - ImplicitSurface is slow when colliding. Can we use BVHs?
• PointCloud - OccupancyGrid is slow when colliding

Correctness

• TriangleMesh - perspective Heightmap can incorrectly return no collision for very large triangles that pass from behind the origin to collide with the heightmap.

Within distance

Availability (in addition to collision detection issues)

• OccupancyGrid - OccupancyGrid isn't implemented -- need to walk around nearby cells
• Heightmap - anything isn't implemented. Should at least be able to do this for points and spheres -- need to walk around nearby cells.

Correctness

• Reported implicit surface elements can be outside of the actual geometry by tolerance

Speed (in addition to collision detection issues)

• PointCloud - PointCloud is slow
• OccupancyGrid - almost anything is slow

Distance

Availability

• OccupancyGrid - anything isn't implemented. Could implement brute-force detection at least for primitives and convex hulls.
• Heightmap - anything isn't implemented. Could implement iterative detection for primitives and convex hulls.

Speed

• point cloud - point cloud is slow
• point cloud - triangle mesh is slow

Contacts

All the weaknesses of WithinDistance are inherited.