MeshesOperations: Operations on 3D Meshes

library(MeshesOperations)
library(SurfaceReconstruction)
library(rgl)

psr <- PoissonReconstruction(cyclide)
shade3d(psr, color="yellow")
ms <- MinkowskiSum(scale3d(cube3d(),1/8,1/8,1/8), psr, normals = TRUE)
rms <- toRGL(ms)
shade3d(rms, color="yellow")
wire3d(rms)

################################################################################
psr <- PoissonReconstruction(SolidMobiusStrip)
shade3d(psr, color="yellow")

ms <- MinkowskiSum(scale3d(cube3d(),1/8,1/8,1/8), psr, normals = TRUE)
rms <- toRGL(ms)
shade3d(rms, color="yellow")
wire3d(rms)

################################################################################
vertices <- rbind(
  c(1.61352, -0.43234, 1.1862),
  c(1.18118, -1.18118, 1.1862),
  c(0.43234, -1.61352, 1.1862),
  c(-0.43234, -1.61352, 1.1862),
  c(-1.18118, -1.18118, 1.1862),
  c(-1.61352, -0.43234, 1.1862),
  c(-1.61352, 0.43234, 1.1862),
  c(-1.18118, 1.18118, 1.1862),
  c(-0.43234, 1.61352, 1.1862),
  c(0.43234, 1.61352, 1.1862),
  c(1.18118, 1.18118, 1.1862),
  c(1.61352, 0.43234, 1.1862),
  c(1.61352, -0.43234, -1.1862),
  c(1.61352, 0.43234, -1.1862),
  c(1.18118, 1.18118, -1.1862),
  c(0.43234, 1.61352, -1.1862),
  c(-0.43234, 1.61352, -1.1862),
  c(-1.18118, 1.18118, -1.1862),
  c(-1.61352, 0.43234, -1.1862),
  c(-1.61352, -0.43234, -1.1862),
  c(-1.18118, -1.18118, -1.1862),
  c(-0.43234, -1.61352, -1.1862),
  c(0.43234, -1.61352, -1.1862),
  c(1.18118, -1.18118, -1.1862),
  c(2.0102, 0.53863, 0),
  c(1.47157, 1.47157, 0),
  c(0.53863, 2.0102, 0),
  c(-0.53863, 2.0102, 0),
  c(-1.47157, 1.47157, 0),
  c(-2.0102, 0.53863, 0),
  c(-2.0102, -0.53863, 0),
  c(-1.47157, -1.47157, 0),
  c(-0.53863, -2.0102, 0),
  c(0.53863, -2.0102, 0),
  c(1.47157, -1.47157, 0),
  c(2.0102, -0.53863, 0),
  c(0.89068, 0.23866, 1.77777),
  c(0.89068, -0.23866, 1.77777),
  c(0.65202, -0.65202, 1.77777),
  c(0.23866, -0.89068, 1.77777),
  c(-0.23866, -0.89068, 1.77777),
  c(-0.65202, -0.65202, 1.77777),
  c(-0.89068, -0.23866, 1.77777),
  c(-0.89068, 0.23866, 1.77777),
  c(-0.65202, 0.65202, 1.77777),
  c(-0.23866, 0.89068, 1.77777),
  c(0.23866, 0.89068, 1.77777),
  c(0.65202, 0.65202, 1.77777),
  c(0.65202, -0.65202, -1.77777),
  c(0.89068, -0.23866, -1.77777),
  c(0.89068, 0.23866, -1.77777),
  c(0.65202, 0.65202, -1.77777),
  c(0.23866, 0.89068, -1.77777),
  c(-0.23866, 0.89068, -1.77777),
  c(-0.65202, 0.65202, -1.77777),
  c(-0.89068, 0.23866, -1.77777),
  c(-0.89068, -0.23866, -1.77777),
  c(-0.65202, -0.65202, -1.77777),
  c(-0.23866, -0.89068, -1.77777),
  c(0.23866, -0.89068, -1.77777),
  c(0, 0, 2.04922),
  c(0, 0, -2.04922)
)
triangles <- lapply(list(
  c(36,60,47),
  c(37,60,36),
  c(38,60,37),
  c(39,60,38),
  c(40,60,39),
  c(41,60,40),
  c(42,60,41),
  c(43,60,42),
  c(44,60,43),
  c(45,60,44),
  c(46,60,45),
  c(47,60,46),
  c(48,61,59),
  c(49,61,48),
  c(50,61,49),
  c(51,61,50),
  c(52,61,51),
  c(53,61,52),
  c(54,61,53),
  c(55,61,54),
  c(56,61,55),
  c(57,61,56),
  c(58,61,57),
  c(59,61,58)
), function(x) x+1)
quads <- lapply(list(
  c(0,11,24,35),
  c(10,25,24,11),
  c(9,26,25,10),
  c(8,27,26,9),
  c(7,28,27,8),
  c(6,29,28,7),
  c(5,30,29,6),
  c(4,31,30,5),
  c(3,32,31,4),
  c(2,33,32,3),
  c(1,34,33,2),
  c(0,35,34,1),
  c(12,35,24,13),
  c(13,24,25,14),
  c(14,25,26,15),
  c(15,26,27,16),
  c(16,27,28,17),
  c(17,28,29,18),
  c(18,29,30,19),
  c(19,30,31,20),
  c(20,31,32,21),
  c(21,32,33,22),
  c(22,33,34,23),
  c(12,23,34,35),
  c(0,37,36,11),
  c(0,1,38,37),
  c(1,2,39,38),
  c(2,3,40,39),
  c(3,4,41,40),
  c(4,5,42,41),
  c(5,6,43,42),
  c(6,7,44,43),
  c(7,8,45,44),
  c(8,9,46,45),
  c(9,10,47,46),
  c(10,11,36,47),
  c(12,49,48,23),
  c(12,13,50,49),
  c(13,14,51,50),
  c(14,15,52,51),
  c(15,16,53,52),
  c(16,17,54,53),
  c(17,18,55,54),
  c(18,19,56,55),
  c(19,20,57,56),
  c(20,21,58,57),
  c(21,22,59,58),
  c(22,23,48,59)
), function(x) x+1)
faces <- c(triangles, quads)
mesh <- list(vertices = vertices, faces = faces)

library(MeshesOperations)
library(rgl)
tLeo <- Mesh(mesh = mesh, triangulate = TRUE)
ms <- MinkowskiSum(dodecahedron3d(), tLeo, triangulate = TRUE) #MinkowskiSum(octahedron3d(), mesh)
x <- Mesh(mesh = ms)
x$edgesDF
edges <- as.matrix(subset(x$edgesDF, angle < 179))[, c("i1", "i2")]

rms <- toRGL(ms)
open3d(windowRect = c(50, 50, 562, 562), zoom = 0.8)
shade3d(rms, color="navy")
plotEdges(ms[["vertices"]], edges, color = "gold",
          tubesRadius = 0.06, spheresRadius = 0.08)