SimplifySurface

Category

Transformation

Function

Simplifies a triangulated surface and resamples data attached to the surface.

Syntax

simplified = SimplifySurface(original_surface, max_error, max_data_error,
                             volume, boundary, length, data, stats);

Inputs

Name	Type	Default	Description
original_surface	field	(none)	triangulated surface
max_error	scalar	input dependent	maximum positional error
max_data_error	scalar	input dependent	maximum data error
volume	flag	1	1: move vertices to preserve volume 0: do not move vertices
boundary	flag	0	1: simplify surface boundaries 0: do not simplify surface boundaries
length	flag	1	1: move vertices to preserve the length of boundaries 0: do not move vertices
data	flag	1	1: use data dependent on "positions" to constrain simplification 0: ignore data for simplification
stats	flag	0	1: provide simple statistics. 0: do not provide statistics

Outputs

Name	Type	Description
simplified	field	simplified triangulated surface

Functional Details

SimplifySurface builds a simplified surface that is guaranteed to deviate from original_surface by less than max_error. This means that each vertex of simplified as well as each point inside a triangle of simplified is at a Euclidean distance no further than max_error from original_surface. Similarly, each vertex of original_surface as well as each point inside a triangle of original_surface is at a distance no further than max_error from the simplified surface.

In addition, if a "data" component of original_surface is dependent on the "positions" component and is not TYPE_STRING, SimplifySurface will perform a data dependent simplification: SimplifySurface will resample "data" on the simplified surface and guarantee that the maximum deviation between the original and re-sampled data is less than max_error_data. For efficiency reasons, the dimensionality of the "data" component is currently limited to 3: for instance, it will work for RGB colors or for gradient values in 3-dimension. Note that data dependent on connections will not constrain simplification.

Vertex normals for the simplified surface are automatically computed.

Components dependent on "positions" or "connections" of original_surface are added to simplified and re-sampled. For components dependent on "connections", the triangle areas are used to weight the resampling.

The following components are not re-sampled: "positions", "connections", "invalid positions", "invalid connections" "normals", "neighbors", and "positional error".

original_surface	must have triangular connections. original_surface is the field that is being simplified.
max_error	maximum distance (in the units of the "position" component) between simplified and original_surface. The default value for max_error is 1% of the diagonal of the bounding box of original_surface. You may decide to set max_error to a lower or higher value than the default.
max_data_error	maximum deviation between data attached to original_surface vertices, and the resampling of that data on the simplified surface. (Again the maximum deviation also holds for points inside triangles, not just vertices). The default value for the maximum error on the data is set to 10% of the diagonal of the bounding box in data space. If the data is one dimensional, the default error is (max_data-min_data)/10. max_data_error is ignored if data = 0 or if the data are connection-dependent.
volume	specifies whether the volume enclosed by the surface should be preserved or not. If set to 1, SimplifySurface will move the surface vertices in order to preserve the volume while the number of vertices is being reduced. In this case, the volume is preserved to within floating point or higher accuracy. If set to 0, the surface vertices will not be moved. The default is 1. The volume is only truly defined for a surface that does not have a boundary (closed surface). Setting volume to 1 on a surface with boundary will have the effect of preventing shrinkage and producing more regular triangles. Note that if several surfaces share the same boundary, as when Isosurface is used on partitioned data, the volume can still be preserved with volume set to 1 if the boundary is left intact (boundary set to 0). With surfaces that present sharp angles, such as CAD data, setting volume to 1 might not work well. In general, we recommend setting volume to zero when operating on CAD data.
boundary	specifies whether the boundary of a surface should be simplified or left intact. If set to 1, then the boundary is simplified while respecting the same errors max_error and max_data_error. If set to 0, then the boundary is left intact. The default is 0. If original_surface has no boundary, this option is ignored.
length	if boundary set to 1, specifies whether the length of the simplified boundary should be preserved. If set to 1, in a manner analogous to volume preservation, SimplifySurface will move the boundary vertices in order to preserve the boundary length while the number of boundary vertices is being reduced. If set to 0, the boundary vertices will not be moved. The default is 1. If boundary is set to 0 then the value of length is ignored.
data	if set to 1, instructs SimplifySurface use max_data_error to constrain simplification if data are dependent on "positions" and are not TYPE_STRING, and if the dimensionality of such data is 3 or lower. If set to 0, simplification will not be constrained by data. In any case, SimplifySurface will resample data after simplification. The default is 1.
stats	if set to 1, instructs SimplifySurface to write simple statistics: number of vertices and triangles in original_surface, number of vertices and triangles in simplified, and percentage of original numbers of vertices and triangles. This information will appear in the Message window. If set to 0, SimplifySurface will not provide statistics. The default is 0.
simplified	simplified surface.

Generating surface levels of detail.

SimplifySurface adds a "positional error" component to the simplified surface. "positional error" is a component dependent on "positions" that provides for each vertex of simplified a positive number. This positive number, the error value, represents the radius of a sphere centered on the vertex, that is guaranteed to intersect the original surface. The union of such spheres represents the error volume of the simplified surface, which is guaranteed to enclose the original surface. Points inside triangles are assigned an error value that is interpolated from the error values at the triangle vertices using barycentric coordinates.

Using the "positional error" component, a simplified surface can be re-simplified to any max_error while still guaranteeing a bound with respect to the original surface. This is useful for generating successive levels of detail.

If the same error bound is used, a marginal additional simplification can be observed: the algorithm implements a greedy method, and does not guarantee to find the minimum number of triangles that respects a given error bound.

The use of the "positional error" component by SimplifySurface is transparent to you, but you may occasionally want to visualize the simplification error, using the Mark module. An example is provided in SimplifySurface.net.

Components

SimplifySurface adds a "positional error" component that is dependent on "positions" (see "Generating surface levels of detail.").

In general simplified has the same components as original_surface except for "invalid positions", "invalid connections", "neighbors", and components that are TYPE_STRING.

Example Visual Programs

SimplifySurface.net

See Also

Refine, Reduce, Isosurface, Map