brol

inst/images/TorusSigma2.R

@@ -66,7 +66,7 @@ torusMesh <- function(nu = 50, nv = 30, rgl = TRUE){
 }
 
 
-mesh <- Rvcg::vcgUpdateNormals(torusMesh(nu = 400, nv = 400))
+mesh <- Rvcg::vcgUpdateNormals(torusMesh(nu = 256, nv = 256))
 
 coords <- function(xyz){
   x <- xyz[, 1L]

inst/images/torus_wp_Sobel.R

@@ -0,0 +1,89 @@
+library(jacobi)
+library(RcppColors)
+
+x <- y <- seq(-4, 0, length.out = 1024L)
+
+f <- function(x, y) {
+  z <- complex(real = x, imaginary = y)
+  wp(z, omega = c(0.5, 0.5 + 0.5i))
+}
+
+Z <- outer(x, y, f)
+img <- colorMap5(Z)
+
+opar <- par(mar = c(0,0,0,0), bg="black")
+plot(c(-100, 100), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -100, -100, 100, 100)
+par(opar)
+
+
+svg("x.svg", width = 16, height = 16)
+opar <- par(mar = c(0,0,0,0), bg = "black")
+plot(c(-100, 100), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -100, -100, 100, 100)
+par(opar)
+dev.off()
+rsvg::rsvg_png(
+  "x.svg", "wp4x4_cm5.png", width = 1024, height = 1024
+)
+
+# Sobelize
+library(imager)
+# transform the raster to an 'imager' image
+im1 <- as.cimg(
+  aperm(
+    array(
+      col2rgb(img) / 255, 
+      dim = c(3, 1024, 1024)
+    ), c(2L, 3L, 1L)
+  )
+)
+# Sobel transformation
+Sobel <- function(im) {
+  M <- rbind(
+    c(-1, -2, -1),
+    c( 0,  0,  0),
+    c( 1,  2,  1)
+  )
+  imX <- convolve(im, as.cimg(M))
+  imY <- convolve(im, as.cimg(t(M)))
+  imXY <- enorm(list(imX, imY))
+  pmax(pmin(imXY, 1), 0)
+}
+# apply Sobel transformation and get the colors as hex codes
+im2 <- Sobel(im1)
+r <- c(squeeze(R(im2)))
+g <- c(squeeze(G(im2)))
+b <- c(squeeze(B(im2)))
+clrs <- rgb(r, g, b)
+
+source("C:/SL/R/imagesProcessing/savePNG.R")
+savePNG(im2, "wp4x4_cm5_Sobel.png", 1024L, 1024L)
+
+
+##################################################################
+library(rgl)
+library(cgalMeshes)
+mesh1 <- torusMesh(
+  R = sqrt(2), r = 1, nu = 1024L, nv = 1024L, conformal = FALSE
+)
+mesh2 <- torusMesh(
+  R = sqrt(2), r = 1, nu = 1024L, nv = 1024L, conformal = TRUE
+)
+#clrs <- c(img)
+mesh1[["material"]] <- mesh2[["material"]] <- list("color" = clrs)
+# plot
+open3d(windowRect = 50 + c(0, 0, 640, 320))
+clear3d(type = "lights") # destroy current lights
+light3d(x = -50, y = 100, z = 100)
+bg3d("#363940")
+mfrow3d(1, 2)
+view3d(-25, -25, zoom = 0.75)
+shade3d(mesh1, specular = "gold")
+next3d()
+view3d(-25, -25, zoom = 0.75)
+shade3d(mesh2, specular = "gold")
+
+snapshot3d("tori_square_wp_Sobel.png", webshot = FALSE)

inst/images/torus_wp_Sobel_rectangular.R

@@ -0,0 +1,91 @@
+library(jacobi)
+library(RcppColors)
+
+x <- y <- seq(-4, 0, length.out = 512L)
+
+f <- function(x, y) {
+  z <- complex(real = x, imaginary = y)
+  wp(z, omega = c(0.5, 0.5 + 0.5i), derivative = 0L)
+}
+
+Z <- outer(x, y, f)
+img <- colorMap5(Z)
+img <- cbind(img, img)
+
+opar <- par(mar = c(0,0,0,0), bg="black")
+plot(c(-200, 200), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -200, -100, 200, 100)
+par(opar)
+
+library(imager)
+
+im1 <- as.cimg(
+  aperm(
+    array(
+      col2rgb(c(img)) / 255, 
+      dim = c(3, 512, 1024)
+    ), c(3L, 2L, 1L)
+  )
+)
+
+
+svg("x.svg", width = 16, height = 8)
+opar <- par(mar = c(0,0,0,0), bg = "black")
+plot(c(-200, 200), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -200, -100, 200, 100)
+par(opar)
+dev.off()
+rsvg::rsvg_png(
+  "x.svg", "wp8x4_cm5_Sobel.png", width = 512, height = 256
+)
+
+# Sobelize
+sobel <- function(im) {
+  M <- rbind(
+    c(-1, -2, -1),
+    c(0, 0, 0),
+    c(1, 2, 1)
+  )
+  imX <- convolve(im, as.cimg(M))
+  imY <- convolve(im, as.cimg(t(M)))
+  imXY <- enorm(list(imX, imY))
+  pmax(pmin(imXY, 1), 0)
+}
+
+im2 <- sobel(im1)
+r <- c(squeeze(R(im2)))
+g <- c(squeeze(G(im2)))
+b <- c(squeeze(B(im2)))
+clrs <- rgb(r, g, b)
+img <- as.raster(im2)
+
+source("C:/SL/R/imagesProcessing/savePNG.R")
+savePNG(im2, "wp8x4_cm5_Sobel.png", 512L, 256L)
+
+
+##################################################################
+library(rgl)
+library(cgalMeshes)
+mesh1 <- torusMesh(
+  R = sqrt(5), r = 1, nu = 1024L, nv = 512L, conformal = FALSE
+)
+mesh2 <- torusMesh(
+  R = sqrt(5), r = 1, nu = 1024L, nv = 512L, conformal = TRUE
+)
+#clrs <- c(img)
+mesh1[["material"]] <- mesh2[["material"]] <- list("color" = clrs)
+# plot
+open3d(windowRect = 50 + c(0, 0, 640, 320))
+clear3d(type = "lights") # destroy current lights
+light3d(x = -50, y = 100, z = 100)
+bg3d("#363940")
+mfrow3d(1, 2)
+view3d(-25, -25, zoom = 0.75)
+shade3d(mesh1, specular = "gold")
+next3d()
+view3d(-25, -25, zoom = 0.75)
+shade3d(mesh2, specular = "gold")
+
+snapshot3d("tori_nonsquare_wp_Sobel.png", webshot = FALSE)

inst/images/wp.R

@@ -0,0 +1,49 @@
+library(jacobi)
+library(RcppColors)
+
+x <- seq(4, 8, len = 1024)-8
+y <- seq(4, 8, len = 1024)-8
+
+f <- function(x, y) {
+  z <- complex(real = x, imaginary = y)
+  wp(z, omega = c(0.5, 0.5+0.5i), derivative = 0L)
+}
+
+Z <- outer(x, y, f)
+img <- colorMap5(Z)
+
+opar <- par(mar = c(0,0,0,0), bg="black")
+plot(c(-100, 100), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -100, -100, 100, 100)
+par(opar)
+
+
+svg("x.svg", width = 16, height = 16)
+opar <- par(mar = c(0,0,0,0), bg = "black")
+plot(c(-100, 100), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
+rasterImage(img, -100, -100, 100, 100)
+par(opar)
+dev.off()
+
+rsvg::rsvg_png(
+  "x.svg", "wp4x4_cm5.png", width = 1024, height = 1024
+)
+
+##################################################################
+library(rgl)
+library(cgalMeshes)
+mesh <- torusMesh(
+  R = sqrt(2), r = 1, nu = 1024, nv = 1024, conformal = FALSE, normals = FALSE
+)
+
+#clrs <- c(img)
+mesh[["material"]] <- list("color" = clrs)
+
+open3d(windowRect = 50 + c(0, 0, 512, 512))
+bg3d("#363940")
+view3d(-25, -25, zoom = 0.75)
+clear3d(type = "lights") # destroy current lights
+light3d(x = -50, y = 100, z = 100)
+shade3d(mesh, specular = "forestgreen")

inst/images/wpprime02.R

@@ -1,33 +1,33 @@
 library(jacobi)
 library(RcppColors)
 
-x <- seq(0, 1, len = 1024)
-y <- seq(0, 1, len = 1024)
+x <- seq(-1, 1, len = 1024)
+y <- seq(-1, 1, len = 1024)
 
 f <- function(x, y) {
   z <- complex(real = x, imaginary = y)
-  wp(z, omega = c(1/2, 1i/2), derivative = 0L)
+  wp(z, g = c(189, 0), derivative = 0L)
 }
 
 Z <- outer(x, y, f)
 img <- colorMap1(Z)
 
 opar <- par(mar = c(0,0,0,0), bg="black")
-plot(c(-100, 100), c(-100, 100), type = "n", 
-     xlab = "", ylab = "", axes = FALSE, asp = 1)
+plot(c(-100, 100), c(-100, 100), type = "n", xaxs ="i", yaxs = "i",
+     xlab = NA, ylab = NA, axes = FALSE, asp = 1)
 rasterImage(img, -100, -100, 100, 100)
 par(opar)
 
 
-svg("x.svg", width = 12, height = 12)
+svg("x.svg", width = 16, height = 8)
 opar <- par(mar = c(0,0,0,0), bg = "black")
 plot(
-  c(-100, 100), c(-100, 100), type = "n", xaxs = "i", yaxs = "i",
+  c(-200, 200), c(-100, 100), type = "n", xaxs = "i", yaxs = "i",
   xlab = NA, ylab = NA, axes = FALSE, asp = 1
 )
-rasterImage(img, -100, -100, 100, 100)
+rasterImage(img, -200, -100, 200, 100)
 par(opar)
 dev.off()
 
-rsvg::rsvg_png("x.svg", "wp.png", width = 1024, height = 1024)
+rsvg::rsvg_png("x.svg", "wp2x1.png", width = 1024, height = 512)