triangulate_matrix: Triangulate a Height Map

In terrainmeshr: Triangulate and Simplify 3D Terrain Meshes

Description

Uses Delaney triangulation to approximate a rectangular height field (in matrix form) with constraints (either maximum allowable error, or a maximum number of triangles). Increasing the error limit will result in a courser approximation, but fewer triangles in the model. For many models (particularly those with large, flat regions or smooth changes in height), this can result in significant reductions in model size with no perceptual loss in terrain surface quality.

Usage

triangulate_matrix(
  heightmap,
  maxError = 1e-04,
  maxTriangles = 0,
  y_up = TRUE,
  start_index = 1,
  verbose = FALSE
)

Arguments

heightmap	A two-dimensional matrix, where each entry in the matrix is the elevation at that point. All points are assumed to be evenly spaced.
maxError	Default '0.0001'. Maximum error allowed in triangulating the height map.
maxTriangles	Default '0', which turns off this setting (and only uses the 'max_error' arg). Otherwise, specifies the maximum number of triangles when triangulating the height map.
y_up	Default 'TRUE'. Which axis is "upwards" in the return matrix. If 'FALSE', 'z' is up.
start_index	Default '1'. The offset to the first 'x' and 'z' indices.
verbose	Default 'FALSE'. Prints reduction in number of triangles/max error.

Value

Returns a matrix of vertices and IDs for each triangle.

Examples

#Let's triangulate the built-in `volcano` dataset.

#Helper function to plot polygons over an `image()` plot.
plot_polys = function(tri_matrix) {
  #reverse orienation for `image`
  tri_matrix[,3] = max(tri_matrix[,3])-tri_matrix[,3]+1
  for(i in seq_len(nrow(tri_matrix)/3)) {
    polypath(tri_matrix[(3*(i-1)+1):(3*i), c(1,3)])
  }
}

#Here, we don't accept any error, but still triangulate
tris = triangulate_matrix(volcano, maxError = 0, verbose = TRUE)
image(x=1:nrow(volcano), y = 1:ncol(volcano), volcano)
plot_polys(tris)

#Let's increase the allowable error:
tris = triangulate_matrix(volcano, maxError = 1, verbose = TRUE)
image(x=1:nrow(volcano), y = 1:ncol(volcano), volcano)
plot_polys(tris)

#Increase it again
tris = triangulate_matrix(volcano, maxError = 10, verbose = TRUE)
image(x=1:nrow(volcano), y = 1:ncol(volcano), volcano)
plot_polys(tris)

#Here, we set an allowable number of triangles instead, using exactly 20 triangles:
tris = triangulate_matrix(volcano, maxTriangles = 20, verbose = TRUE)
image(x=1:nrow(volcano), y = 1:ncol(volcano), volcano)
plot_polys(tris)

#The output of this function can be passed directly to `rgl::triangles3d()` for plotting in 3D.

Example output

35.0% reduction: Number of triangles reduced from 10614 to 6904. Error: 0.000000
82.4% reduction: Number of triangles reduced from 10614 to 1867. Error: 1.000000
99.1% reduction: Number of triangles reduced from 10614 to 92. Error: 9.666672
99.8% reduction: Number of triangles reduced from 10614 to 20. Error: 28.664627

terrainmeshr documentation built on April 29, 2020, 5:06 p.m.