9.93. Interpolate Point Cloud to Regular Grid

Group (Subgroup)

Sampling (Interpolation)

Description

This Filter interpolates the values of arrays stored in a Vertex Geometry (point cloud) onto a user-selected Image Geometry (regular grid). For each point in the cloud, the filter applies a kernel centered on the point’s voxel and accumulates weighted contributions into every voxel the kernel overlaps. The result is a single interpolated value per voxel per array, computed as a weighted average of all contributions.

Kernel

The user defines the (x, y, z) radii of a kernel in real space units. The kernel can be initialized to one of two modes:

• Uniform – Every voxel within the kernel radius receives equal weight (1.0).

• Gaussian - Voxel weights fall off with distance from the center according to a Gaussian function controlled by user-specified sigmas in each dimension.

The kernel radii are converted to voxel units based on the spacing of the Image Geometry. If the kernel radius in a given dimension is smaller than the voxel spacing, the kernel has a zero extent in that dimension (i.e., each point only affects its own voxel along that axis).

Algorithm

The interpolation proceeds in two passes:

Pass 1 – Accumulation (one iteration over all vertices):

1. For each vertex in the Vertex Geometry, compute the destination voxel index from the vertex coordinates and the Image Geometry’s origin, spacing, and dimensions. Vertices that fall outside the grid are silently skipped.

2. If a mask is enabled and the vertex is masked out, skip it.

3. Center the kernel on that voxel and determine the kernel bounds, clipped to the grid extents.

4. For each voxel within the clipped kernel:

   • Look up the kernel weight using the 3D offset from the center voxel.

   • For each interpolated array: multiply the source value by the kernel weight and accumulate the weighted value, the weight itself and any enabled statistics into the destination voxel.

   • For each copied array: accumulate the source value with uniform weight (1.0) regardless of the selected kernel type.

Pass 2 – Finalization (one iteration over all voxels):

For each voxel that received at least one contribution:

• The interpolated output value is sum(weight * value) / sum(weight).

• Any enabled statistics are written from the accumulated state.

Arrays to Interpolate vs. Arrays to Copy

Both options transfer data from the Vertex Geometry onto the Image Geometry, but they differ in how the kernel is applied:

• Arrays to Interpolate use the selected kernel (Uniform or Gaussian). The kernel weight multiplies each vertex’s value before being accumulated into surrounding voxels. The final output is a kernel-weighted average. Optional statistics (length, min, max, mean, standard deviation, summation) can be computed on the weighted contributions. The output array type is always float64 because the weighted average produces floating-point values regardless of the input type.

• Arrays to Copy always use a uniform kernel (weight = 1.0), even when Gaussian interpolation is selected. The final output is a simple arithmetic average of all values that fell within the kernel radius. No statistics are computed for copied arrays. The output array type matches the source array type.

Use Arrays to Interpolate for data values that should be smoothed or blended by the kernel (e.g., measured scalar fields). Use Arrays to Copy for categorical or index data where Gaussian weighting would not be meaningful.

All arrays selected for interpolation or copying must be scalar (single-component) arrays.

Inline Statistics

Rather than storing all per-voxel contributions and computing statistics in a separate filter, this filter can compute the following statistics inline during the accumulation pass. Each statistic is optional and controlled by a boolean parameter. When enabled, an additional output array is created for each interpolated array with the array name plus a configurable suffix (e.g., FaceAreas_Length).

Statistic	Output Type	Description
Length	uint64	Number of weighted contributions to the voxel
Minimum	float32	Smallest weighted value (weight * source_value)
Maximum	float32	Largest weighted value
Mean	float32	Arithmetic mean of weighted values (sum / count)
Standard Deviation	float32	Population standard deviation of weighted values, computed via Welford’s numerically stable online algorithm
Summation	float32	Sum of all weighted values

Statistics are computed on the weighted values (kernel_weight * source_value), which are the same quantities that contribute to the interpolated average. Voxels with no contributions receive a value of zero for all statistics.

Median is not supported because it requires storing every vertex’s contribution, which would negate the memory savings of the flat accumulation approach.

Mask

An optional boolean mask array may be provided. Vertices where the mask value is false are skipped entirely during interpolation – they do not contribute to any voxel’s accumulated value or statistics.

Memory Usage

This filter uses flat arrays rather than variable-length lists, so memory usage is proportional to the number of voxels in the Image Geometry (not the number of points times the kernel size). For each interpolated array, the filter temporarily allocates ~56 bytes per voxel for accumulation state. For each copied array, ~16 bytes per voxel is allocated. These temporary variables are freed after the finalization pass.

Voxel Index Computation

The destination voxel for each vertex is computed on-the-fly from the vertex coordinates and the Image Geometry’s origin, spacing, and dimensions. There is no need to pre-compute a voxel indices array (e.g., via the Map Point Cloud to Regular Grid filter). Vertices whose coordinates fall outside the Image Geometry bounds are silently skipped.

Input Parameter(s)

Parameter Name	Parameter Type	Parameter Notes	Description
Use Mask Array	Bool		Specifies whether or not to use a mask array
Interpolation Technique	Choices		Selected Interpolation Technique
Kernel Size	Vector of Float32 Values	Order=x,y,z	Specifies the kernel size
Gaussian Sigmas	Vector of Float32 Values	Order=x,y,z	Specifies the Gaussian sigmas

Destination Image Geometry

Parameter Name	Parameter Type	Parameter Notes	Description
Interpolated Image Geometry	Geometry Selection	Image	DataPath to interpolated geometry

Input Vertex Geometry

Parameter Name	Parameter Type	Parameter Notes	Description
Vertex Geometry to Interpolate	Geometry Selection	Vertex	DataPath to geometry to interpolate
Mask	Array Selection	Allowed Types: boolean Comp. Shape: 1	DataPath to the boolean mask array. Values that are true will mark that vertex as usable.
Attribute Arrays to Interpolate	MultiArraySelection		DataPaths to interpolate
Attribute Arrays to Copy	MultiArraySelection		DataPaths to copy

Output Data Object(s)

Parameter Name	Parameter Type	Parameter Notes	Description

Statistics Options

Parameter Name	Parameter Type	Parameter Notes	Description
Find Length	Bool		Compute the number of contributions per voxel
Find Minimum	Bool		Compute the minimum weighted value per voxel
Find Maximum	Bool		Compute the maximum weighted value per voxel
Find Mean	Bool		Compute the mean weighted value per voxel
Find Standard Deviation	Bool		Compute the standard deviation of weighted values per voxel
Find Summation	Bool		Compute the sum of weighted values per voxel
Length Suffix	DataObjectName		Suffix appended to array name for length output
Minimum Suffix	DataObjectName		Suffix appended to array name for minimum output
Maximum Suffix	DataObjectName		Suffix appended to array name for maximum output
Mean Suffix	DataObjectName		Suffix appended to array name for mean output
Standard Deviation Suffix	DataObjectName		Suffix appended to array name for standard deviation output
Summation Suffix	DataObjectName		Suffix appended to array name for summation output

License & Copyright

Please see the description file distributed with this plugin.

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