rgl package R test

thingiverse

Testing the functionality of the rgl package in R involves merging two fundamental polyhedra - the icosahedron and the cube. To execute this test, first install and load the necessary library by running `install.packages("rgl")` followed by `library(rgl)`. Here's how to create these shapes: 1. Icosahedron: Start with a regular icosahedron having 20 triangular faces, 30 edges, and 12 vertices. This can be achieved using the `plot3d()` function in combination with a matrix of vertex coordinates for each shape. 2. Cube: Next, create a cube using the same approach as the icosahedron. The cube has 6 square faces, 12 edges, and 8 vertices. To merge these shapes into one object, you need to define their common vertex set. This requires calculating the overlap between both shapes' vertex coordinates. After defining your custom function for the shapes and identifying overlapping points, combine them using a method such as `rgl::union()`. This function takes two 3D objects as arguments and merges them into one solid object while maintaining all edges from both inputs. Here's an example of how to test this by combining these polyhedra: ```r # Install the rgl package if you haven't already install.packages("rgl") # Load the rgl library library(rgl) # Define a function for creating and plotting 3D shapes create_shape <- function(shape_type, side_length = 1) { # Calculate vertex coordinates based on shape type vertices <- switch( shape_type, cube = matrix(c(-side_length/2, -side_length/2, -side_length/2, +side_length/2, -side_length/2, -side_length/2, +side_length/2, +side_length/2, -side_length/2, -side_length/2, +side_length/2, -side_length/2, -side_length/2, -side_length/2, side_length/2, +side_length/2, -side_length/2, side_length/2, +side_length/2, +side_length/2, side_length/2, -side_length/2, +side_length/2, side_length/2), nrow = 8), icosahedron = matrix(c(-1.0000, -0.9511, -0.3090, -0.8090, +0.5882, -0.3090, +0.3090, +0.9511, -0.3090, +0.9511, -0.3090, +0.3090, -0.9511, -0.3090, +0.3090, -0.8090, +0.5882, +0.3090, +0.3090, +0.9511, +0.3090, -0.5878, -0.9511, +0.3090), nrow = 12) ) # Plot the shape plot3d(vertices[, 1], vertices[, 2], vertices[, 3], type = "n", xlim = c(-side_length/2, side_length/2), ylim = c(-side_length/2, side_length/2), zlim = c(-side_length/2, side_length/2)) # Add edges for (i in 1:nrow(vertices)) { for (j in i+1:nrow(vertices)) { v <- vertices[i, ] + vertices[j, ] lines3d(v[1:3], col = "blue") } } } # Create and merge the shapes create_shape("cube", side_length = 2) create_shape("icosahedron", side_length = 0.5) # Identify overlapping points (vertices) overlap_vertices <- intersect(rgl::coordinates(cube), rgl::coordinates(icosahedron)) # Merge the shapes using union() union_shape <- rgl::union(cube, icosahedron) # Plot the merged shape plot3d(union_shape, type = "n", xlim = c(-side_length/2, side_length/2), ylim = c(-side_length/2, side_length/2), zlim = c(-side_length/2, side_length/2)) for (i in 1:nrow(vertices)) { for (j in i+1:nrow(vertices)) { v <- vertices[i, ] + vertices[j, ] lines3d(v[1:3], col = "blue") } } ```