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## Lighting functions are functions of the form
##
## lighting(normals, view, light, color, color2, material)
##
## with
##
## normals a matrix of unit normal vectors as computed by triangleNormals
## view vector pointing to the viewer
## light vector pointing to the light source
## color color or vector of n colors for the sides of the triangles
## in the direction of to the normal vectors
## color2 color or vector of n colors for the sides of the triangles
## in the opposite direction of to the normal vectors. NA means
## same as 'color'
## alpha the alpha level to use
## material material parameters controlling the lighting calculation.
##
## lighting functions return a vector of n rgb colors corresponding
## to the sides of the trinagles facing the viewer and the lighting
## algorithm.
## phongLighting implements a simple version of the Phong lighting
## model (not shading--that would involve interpolation within the
## triangles). It incorporates ambient and diffuse light, which are
## the same color as the object, and specular light, which is a convex
## combination of the object color and the (white) light color. This
## is based roughly on the description in Foley and Van Dam.
phongLighting <- function(normals, view, light, color, color2, alpha,
material = "default") {
if (length(light) == 4) {
LI <- light[4]
light <- light[1:3]
}
else LI <- 1
if (is.character(material))
material <- getMaterial(material)
ambient <- material$ambient
diffuse <- material$diffuse
specular <- material$specular
exponent <- material$exponent
sr <- material$sr
V <- view / sqrt(sum(view^2))
L <- light / sqrt(sum(light^2))
H <- (L + V) / sqrt(sum((L + V)^2))
sgn <- as.vector(normals %*% V) > 0
N <- ifelse(sgn,1, -1) * normals
Is <- as.vector(specular * abs(N %*% H) ^ exponent)
Id <- as.vector(diffuse * pmax(N %*% L,0))
rgbcol <- t(col2rgb(ifelse(sgn, color, color2)) / 255)
Lrgbcol <- pmin(LI * ((ambient + Id + sr * Is) * rgbcol + (1 - sr) * Is),
1)
Lrgbcol[is.na(Lrgbcol)] <- 0
rgb(Lrgbcol[,1], Lrgbcol[,2], Lrgbcol[,3], alpha)
}
## A simple data base is used to register properties of named
## materials. Some initial entries are based on valuaes for similarly
## named materials in Matlab.
materials.database <- new.env(hash = TRUE)
registerMaterial <- function(name, ambient = 0.3, diffuse = 0.7,
specular = 0.1, exponent = 10, sr = 0) {
value <- list(ambient = ambient, diffuse = diffuse,
specular = specular, exponent = exponent, sr = sr)
assign(name, value, materials.database)
}
getMaterial <- function(name) {
if (exists(name, materials.database, inherits = FALSE))
get(name, materials.database)
else get("default", materials.database, inherits = FALSE)
}
registerMaterial("shiny", ambient = 0.3, diffuse = 0.6, specular = 0.9,
exponent = 20, sr = 0)
registerMaterial("dull", ambient = 0.3, diffuse = 0.8, specular = 0.0,
exponent = 10, sr = 0)
registerMaterial("metal", ambient = 0.3, diffuse = 0.3, specular = 1.0,
exponent = 25, sr = 0.5)
registerMaterial("default", ambient = 0.3, diffuse = 0.7, specular = 0.1,
exponent = 10, sr = 0)
# Alternate version of metal, about 50% brighter?
registerMaterial("metal", ambient = 0.45, diffuse = 0.45, specular = 1.5,
exponent = 25, sr = 0.5)
# 50% would be 0.45 0.45 1.50?
# Alternate version of shiny, about 20% brighter?
registerMaterial("shiny", ambient = 0.36, diffuse = 0.72, specular = 1.08,
exponent = 20, sr = 0)
## perspLighting is an implementation of the lighting algorithm
## described in the help page for persp(). The 'shade' parameter of
## persp is here named 'exponent'. It _looks_ like the shade parameter
## used in persp may be closer to twice the value supplied to persp;
## that is, perspLighting with shade = x seems to be comparable to
## persp() with shade = x / 2. Needed to rename shade to exponent.
## Division by 8 may make this exponent vaguely comparable to the
## Phong one.
perspLighting <- function(normals, view, light, color, color2, alpha,
material = "default") {
if (length(light) == 4) {
LI <- light[4]
light <- light[1:3]
}
else LI <- 1
if (is.character(material))
material <- getMaterial(material)
exponent <- material$exponent
V <- view / sqrt(sum(view^2))
L <- light / sqrt(sum(light^2))
sgn <- as.vector(normals %*% V) > 0
N <- ifelse(sgn,1, -1) * normals
I <- ((1 + as.vector(pmax(N %*% L, 0))) / 2) ^ (exponent / 8)
Lrgbcol <- I * LI * t(col2rgb(ifelse(sgn, color, color2)) / 255)
rgb(Lrgbcol[,1], Lrgbcol[,2], Lrgbcol[,3], alpha)
}
triangleNormalsPhong <- function(triangles) {
N <- triangleNormals(triangles)
ve <- t2ve(triangles)
vt <- vertexTriangles(ve)
VN <- vertexNormals(vt, N)
interpolateVertexNormals(VN, ve$ib)
}
triangleNormalsPhongEX <- function(triangles, reps = 1) {
N <- triangleNormals(triangles)
ve <- t2ve(triangles)
vt <- vertexTriangles(ve)
VN <- vertexNormals(vt, N)
vb <- ve$vb
ib <- ve$ib
n.tri <- nrow(N)
while (reps > 0) {
reps <- reps - 1
n.ver <- nrow(VN)
mt <- triangleMidTriangles(vb, ib, VN)
vb <- cbind(vb, mt$vb)
VN <- rbind(VN, mt$VN)
mtib <- mt$ib + n.ver
ib <- matrix(rbind(ib[1,], mtib[1,],mtib[3,],
mtib[1,], ib[2,],mtib[2,],
mtib[2,], ib[3,], mtib[3,],
mtib),
nrow = 3)
for (i in seq(along = triangles))
if (length(triangles[[i]]) == n.tri)
triangles[[i]] <- rep(triangles[[i]], each = 4)
n.tri <- 4 * n.tri
}
triangles$N <- interpolateVertexNormals(VN, ib)
triangles$v1 <- t(vb[,ib[1,]])
triangles$v2 <- t(vb[,ib[2,]])
triangles$v3 <- t(vb[,ib[3,]])
triangles
}
# version that handles color interpolation
# **** could lift out and triangleEdges calls
triangleNormalsPhongEX <- function(triangles, reps = 1) {
N <- triangleNormals(triangles)
ve <- t2ve(triangles)
vt <- vertexTriangles(ve)
VN <- vertexNormals(vt, N)
vb <- ve$vb
ib <- ve$ib
n.tri <- nrow(N)
color <- rep(triangles$color, length = n.tri)
color2 <- rep(triangles$color2, length = n.tri)
col.mesh <- rep(triangles$col.mesh, length = n.tri)
color2 <- ifelse(is.na(color2), color, color2)
col.mesh <- ifelse(is.na(col.mesh), color, col.mesh)
VC <- vertexColors(vt, color)
VC2 <- vertexColors(vt, color2)
VCm <- vertexColors(vt, col.mesh)
while (reps > 0) {
reps <- reps - 1
n.ver <- nrow(VN)
edges <- triangleEdges(vb, ib)
VC <- rbind(VC, (VC[edges[1,],] + VC[edges[2,],]) / 2)
VC2 <- rbind(VC2, (VC2[edges[1,],] + VC2[edges[2,],]) / 2)
VCm <- rbind(VCm, (VCm[edges[1,],] + VCm[edges[2,],]) / 2)
mt <- triangleMidTriangles(vb, ib, VN)
vb <- cbind(vb, mt$vb)
VN <- rbind(VN, mt$VN)
mtib <- mt$ib + n.ver
ib <- matrix(rbind(ib[1,], mtib[1,],mtib[3,],
mtib[1,], ib[2,],mtib[2,],
mtib[2,], ib[3,], mtib[3,],
mtib),
nrow = 3)
for (i in seq(along = triangles))
if (length(triangles[[i]]) == n.tri)
triangles[[i]] <- rep(triangles[[i]], each = 4)
n.tri <- 4 * n.tri
}
triangles$color <- interpolateVertexColors(VC, ib)
triangles$color2 <- interpolateVertexColors(VC2, ib)
triangles$color.mesh <- interpolateVertexColors(VCm, ib)
triangles$N <- interpolateVertexNormals(VN, ib)
triangles$v1 <- t(vb[,ib[1,]])
triangles$v2 <- t(vb[,ib[2,]])
triangles$v3 <- t(vb[,ib[3,]])
triangles
}
lightTriangles <- function(triangles, lighting, light) {
view <- c(0, 0, 1)
normals <- triangleNormals(triangles)
smooth <- if (is.null(triangles$smooth)) 0 else triangles$smooth
if (smooth == 0)
normals <- triangleNormals(triangles)
else if (smooth == 1)
normals <- triangleNormalsPhong(triangles)
else {
triangles <- triangleNormalsPhongEX(triangles, reps = smooth - 1)
normals <- triangles$N
}
n.tri <- nrow(normals)
color <- rep(triangles$color, length = n.tri)
color2 <- rep(triangles$color2, length = n.tri)
color2 <- ifelse(is.na(color2), color, color2)
alpha <- rep(triangles$alpha, length = n.tri)
mat <- triangles$material
triangles$col.light <- lighting(normals, view, light, color, color2,
alpha, mat)
triangles
}
lightScene <- function(scene, lighting, light) {
if (is.Triangles3D(scene))
lightTriangles(scene, lighting, light)
else lapply(scene, lightTriangles, lighting, light)
}
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