Rebuilt Sampling Patterns and fixed VRAM graph

I decided to rebuild the graphics for the sampling patterns in R. This made it easier to place points at the desired coordinates and to maintain consistent characteristics.
Also updated the Means + VRAM graph, moving the legend over. (The script already did this but the PDF used was out of date.)

Data and Graphics/Sampling Patterns/Sampling Pattern Plots.r

@@ -0,0 +1,345 @@
+library(ggplot2)
+#	the coordinates for the sample positions are based on the DirectX standard sampling positions found here:
+#		https://docs.microsoft.com/en-us/windows/win32/api/d3d11/ne-d3d11-d3d11_standard_multisample_quality_levels
+#	Microsoft uses an upside-down Y-axis in those patterns, but that is corrected here
+
+FAC2NUM	=	function(FRAME, COLS)	{
+	for (place in COLS)	{
+		FRAME[, place]	=	as.numeric(as.character(FRAME[, place]))
+	}
+	return(FRAME)
+}
+
+if	(interactive())	{
+	setwd("E:/Users/Jim/My Documents/OCC/@Reviews/Serious Statistics AA/@1.1 Stuff/Sampling Patterns 1.1/R Output")
+}	else	{
+	pdf(NULL)
+}
+
+theme_set(theme_grey(base_size = 22))
+
+gWIDTH	=	16
+gHEIGH	=	9
+DPI		=	120
+
+customSave	=	function(type="", device=ggdevice, plot = last_plot(), width=gWIDTH, height=gHEIGH, dpi=DPI)	{
+	if	(device	==	"png"	|	device == "both")	{
+		ggsave(filename=paste0("Sample Patterns - ", type, ".png"), plot = plot, device="png", width=width, height=height, dpi=dpi)
+	}
+	if	(device	==	"pdf"	|	device == "both")	{
+		ggsave(filename=paste0("Sample Patterns - ", type, ".pdf"), plot = plot, device="pdf", width=width, height=height)
+	}
+}
+
+BORD	=	list(
+	geom_segment(x = -8,	xend = 8,	y = 8,	yend = 8,												size = 1),
+	geom_segment(x = -8,	xend = 8,	y = 0,	yend = 0,	color = "darkgrey",							size = 1),
+	geom_segment(x = -8,	xend = -8,	y = -8,	yend = 8,												size = 1),
+	geom_segment(x = -8,	xend = 8,	y = -8,	yend = -8,						linetype = "dashed",	size = 1),
+	geom_segment(x = 0,		xend = 0,	y = -8,	yend = 8,	color = "darkgrey",							size = 1),
+	geom_segment(x = 8,		xend = 8,	y = -8,	yend = 8,						linetype = "dashed",	size = 1)
+)
+
+
+AXES = function(SAMPLE = 16)	{
+	list(
+		scale_x_continuous(name = NULL, limits = c(-8, 8), breaks = seq(-8, 7, by = 16/SAMPLE), minor_breaks = NULL, labels = NULL, expand = c(0,0)), 
+		scale_y_continuous(name = NULL, limits = c(-8, 8), breaks = seq(-8, 7, by = 16/SAMPLE), minor_breaks = NULL, labels = NULL, expand = c(0,0)), 
+		scale_color_manual(guide = "legend", name = "", values = c("Sample" = "red", "Tap" = "cyan"), breaks = c("Sample", "Tap")),
+		theme(legend.position = c(1, 0.98), legend.direction="horizontal", legend.justification = c(1,-1), legend.background = element_rect(NA)),
+		coord_fixed(ratio = 1),
+		theme(axis.ticks = element_blank())
+	)
+}
+
+LINES	=	list(
+	geom_hline(aes(yintercept = y),							color = "blue",	linetype = "dashed",	size = 2), 
+	geom_vline(aes(xintercept = x),							color = "blue",	linetype = "dashed",	size = 2), 
+	geom_abline(aes(slope = Slope, intercept = Intercept),	color = "blue", linetype = "dashed",	size = 2)
+)
+
+
+ORDER2x	=	c("Vertical", "Horizontal", "Diagonal (Down)", "Diagonal (Up)", "Quincunx")
+DATA2x	=	as.data.frame(rbind(
+	c(0,	4,		"Vertical",			"Sample"),
+	c(0,	-4,		"Vertical",			"Sample"),
+
+	c(-4,	0,		"Horizontal",		"Sample"),
+	c(4,	0,		"Horizontal",		"Sample"),
+
+	c(-4,	4, 		"Diagonal (Down)",	"Sample"),
+	c(4,	-4, 	"Diagonal (Down)",	"Sample"),
+
+	c(-4,	-4, 	"Diagonal (Up)",	"Sample"),
+	c(4,	4, 		"Diagonal (Up)",	"Sample"),
+
+	c(-8,	8,		"Quincunx",			"Sample"),
+	c(0,	0,		"Quincunx",			"Sample"),
+	c(-8,	-8,		"Quincunx",			"Tap"),
+	c(8,	-8,		"Quincunx",			"Tap"),
+	c(8,	8,		"Quincunx",			"Tap")
+)	)
+LINES2x = as.data.frame(rbind(
+	c(0, 	NA,	NA,	NA,	"Vertical"),
+	c(NA,	0,	NA,	NA,	"Horizontal"),
+	c(NA,	NA,	-1,	0,	"Diagonal (Down)"),
+	c(NA,	NA,	1,	0,	"Diagonal (Up)"),
+	c(NA,	NA,	NA,	NA,	"Quincunx")
+)	)
+
+DATA2x		=	FAC2NUM(DATA2x, 1:2)
+DATA2x[,3]	=	factor(DATA2x[,3], levels = ORDER2x, ordered = TRUE)
+colnames(DATA2x)	=	c("x", "y", "Pattern", "Type")
+
+LINES2x	=	FAC2NUM(LINES2x, 1:4)
+LINES2x[,5]	=	factor(LINES2x[,5], levels = ORDER2x, ordered = TRUE)
+colnames(LINES2x)	=	c("x", "y", "Slope", "Intercept", "Pattern")
+
+SAMPLE	=	2
+
+ggplot(data = LINES2x, aes(x = x, y = y)) + 
+ggtitle("2x Sample Patterns") + 
+BORD + LINES + 
+geom_point(data = DATA2x, aes(color = Type), size = 7) + 
+facet_grid(cols = vars(Pattern)) + AXES(SAMPLE)
+
+customSave("2x", "both")
+
+
+ORDER4x	=	c("Ordered", "Rotated", "Diagonal", "Rook (1)", "Rook (2)", "Queen", "Quincunx")
+D	=	8/sqrt(2)
+DATA4x	=	as.data.frame(rbind(
+	c(-4,	4,		"Ordered",	"",				"Sample"),
+	c(-4,	-4,		"Ordered",	"",				"Sample"),
+	c(4,	-4,		"Ordered",	"",				"Sample"),
+	c(4,	4,		"Ordered",	"",				"Sample"),
+
+	c(-D,	0,		"Rotated",	"",				"Sample"),
+	c(D,	0,		"Rotated",	"",				"Sample"),
+	c(0,	-D,		"Rotated",	"",				"Sample"),
+	c(0,	D,		"Rotated",	"",				"Sample"),
+
+	c(-6,	6,	"Diagonal",	"",				"Sample"),
+	c(-2,	2,	"Diagonal",	"",				"Sample"),
+	c(2,	-2,	"Diagonal",	"",				"Sample"),
+	c(6,	-6,	"Diagonal",	"",				"Sample"),
+
+	c(-6,	-6,	"Diagonal",	"Reflection",	"Sample"),
+	c(-2,	-2,	"Diagonal",	"Reflection",	"Sample"),
+	c(2,	2,	"Diagonal",	"Reflection",	"Sample"),
+	c(6,	6,	"Diagonal",	"Reflection",	"Sample"),
+
+	c(-6,	6,		"Rook (1)",	"",				"Sample"),
+	c(-2,	-2,		"Rook (1)",	"",				"Sample"),
+	c(2,	2,		"Rook (1)",	"",				"Sample"),
+	c(6,	-6,		"Rook (1)",	"",				"Sample"),
+
+	c(-6,	-6,		"Rook (1)",	"Reflection",	"Sample"),
+	c(-2,	2,		"Rook (1)",	"Reflection",	"Sample"),
+	c(2,	-2,		"Rook (1)",	"Reflection",	"Sample"),
+	c(6,	6,		"Rook (1)",	"Reflection",	"Sample"),
+
+	c(-6,	2,		"Rook (2)",	"",				"Sample"),
+	c(-2,	6,		"Rook (2)",	"",				"Sample"),
+	c(2,	-6,		"Rook (2)",	"",				"Sample"),
+	c(6,	-2,		"Rook (2)",	"",				"Sample"),
+
+	c(-6,	-2,		"Rook (2)",	"Reflection",	"Sample"),
+	c(-2,	-6,		"Rook (2)",	"Reflection",	"Sample"),
+	c(2,	6,		"Rook (2)",	"Reflection",	"Sample"),
+	c(6,	2,		"Rook (2)",	"Reflection",	"Sample"),
+
+	c(-6,	-2,		"Queen",	"",				"Sample"),
+	c(-2,	6,		"Queen",	"",				"Sample"),
+	c(2,	-6,		"Queen",	"",				"Sample"),
+	c(6,	2,		"Queen",	"",				"Sample"),
+
+	c(-6,	2,		"Queen",	"Reflection",	"Sample"),
+	c(-2,	-6,		"Queen",	"Reflection",	"Sample"),
+	c(2,	6,		"Queen",	"Reflection",	"Sample"),
+	c(6,	-2,		"Queen",	"Reflection",	"Sample"),
+
+	c(-8,	8,		"Quincunx",	"",				"Sample"),
+	c(-8,	0,		"Quincunx",	"",				"Sample"),
+	c(0,	8,		"Quincunx",	"",				"Sample"),
+	c(0,	0,		"Quincunx",	"",				"Sample"),
+	c(-8,	-8,		"Quincunx",	"",				"Tap"),
+	c(0,	-8,		"Quincunx",	"",				"Tap"),
+	c(8,	-8,		"Quincunx",	"",				"Tap"),
+	c(8,	0,		"Quincunx",	"",				"Tap"),
+	c(8,	8,		"Quincunx",	"",				"Tap")
+)	)
+LINES4x = as.data.frame(rbind(
+	c(4, 	NA,		NA,	NA,		"Ordered", ""),
+	c(-4,	NA,		NA,	NA,		"Ordered", ""),
+	c(NA,	4,		NA,	NA,		"Ordered", ""),
+	c(NA,	-4,		NA,	NA,		"Ordered", ""),
+
+	c(NA, 	NA,		1,	D,		"Rotated", ""),
+	c(NA,	NA,		1,	-D,		"Rotated", ""),
+	c(NA,	NA,		-1,	-D,		"Rotated", ""),
+	c(NA,	NA,		-1,	D,		"Rotated", ""),
+
+	c(NA, 	NA,		-1,	0,		"Diagonal", ""),
+	c(NA, 	NA,		1,	0,		"Diagonal", "Reflection"),
+
+	c(NA, 	NA,		NA,	NA,		"Rook (1)",	""),
+	c(NA, 	NA,		NA,	NA,		"Rook (1)",	"Reflection"),
+	c(NA, 	NA,		NA,	NA,		"Rook (2)",	""),
+	c(NA, 	NA,		NA,	NA,		"Rook (2)",	"Reflection"),
+	c(NA, 	NA,		NA,	NA,		"Queen",	""),
+	c(NA, 	NA,		NA,	NA,		"Queen",	"Reflection"),
+	c(NA, 	NA,		NA,	NA,		"Quincunx",	"")
+)	)
+
+DATA4x		=	FAC2NUM(DATA4x, 1:2)
+DATA4x[,3]	=	factor(DATA4x[,3], levels = ORDER4x, ordered = TRUE)
+colnames(DATA4x)	=	c("x", "y", "Pattern", "Reflection", "Type")
+
+LINES4x	=	FAC2NUM(LINES4x, 1:4)
+colnames(LINES4x)	=	c("x", "y", "Slope", "Intercept", "Pattern", "Reflection")
+LINES4x[,5]	=	factor(LINES4x[,5], levels = ORDER4x, ordered = TRUE)
+
+SAMPLE	=	4
+
+ggplot(data = LINES4x, aes(x = x, y = y)) + 
+ggtitle("4x Sample Patterns") + 
+BORD + LINES + 
+geom_point(data = DATA4x, aes(color = Type), size = 7) + 
+facet_grid(cols = vars(Pattern), rows = vars(Reflection)) + AXES(SAMPLE)
+
+customSave("4x", "both", width = 7/5*16)
+
+
+ORDERMS	=	c("2x", "4x", "8x", "16x")
+DATAMS	=	as.data.frame(rbind(
+	c(-4,	4,	"2x"),
+	c(4,	-4,	"2x"),
+
+	c(-6,	-2,	"4x"),
+	c(-2,	6,	"4x"),
+	c(2,	-6,	"4x"),
+	c(6,	2,	"4x"),
+
+	c(-7,	1,	"8x"),
+	c(-5,	-5,	"8x"),
+	c(-3,	5,	"8x"),
+	c(-1,	-3,	"8x"),
+	c(1,	3,	"8x"),
+	c(3,	-7,	"8x"),
+	c(5,	-1,	"8x"),
+	c(7,	7,	"8x"),
+
+	c(-8,	0,	"16x"),
+	c(-7,	8,	"16x"),
+	c(-6,	-4,	"16x"),
+	c(-5,	2,	"16x"),
+	c(-4,	6,	"16x"),
+	c(-3,	-2,	"16x"),
+	c(-2,	-6,	"16x"),
+	c(-1,	3,	"16x"),
+	c(0,	7,	"16x"),
+	c(1,	-1,	"16x"),
+	c(2,	-5,	"16x"),
+	c(3,	5,	"16x"),
+	c(4,	1,	"16x"),
+	c(5,	-3,	"16x"),
+	c(6,	7,	"16x"),
+	c(7,	4,	"16x")
+)	)
+
+LINESMS = as.data.frame(rbind(
+	c(NA, 	NA,		NA,	NA,		"2x",	""),
+	c(NA, 	NA,		NA,	NA,		"4x",	""),
+	c(NA, 	NA,		NA,	NA,		"8x",	""),
+	c(NA, 	NA,		NA,	NA,		"16x",	"")
+)	)
+
+DATAMS		=	FAC2NUM(DATAMS, 1:2)
+DATAMS[,3]	=	factor(DATAMS[,3], levels = ORDERMS, ordered = TRUE)
+colnames(DATAMS)	=	c("x", "y", "Pattern")
+
+LINESMS	=	FAC2NUM(LINESMS, 1:4)
+colnames(LINESMS)	=	c("x", "y", "Slope", "Intercept", "Pattern")
+LINESMS[,5]	=	factor(LINESMS[,5], levels = ORDERMS, ordered = TRUE)
+
+
+ggplot(data = LINESMS, aes(x = x, y = y)) + 
+ggtitle("DirectX Standard Sample Patterns") + 
+BORD + LINES + 
+geom_point(data = DATAMS, color = "red", size = 7) + 
+facet_grid(cols = vars(Pattern)) + AXES()
+
+customSave("MS Standard Patterns", "both", width = 4/5*16)
+
+
+NAMES	=	c("x", "y", "Pattern", "Type")
+
+QUADS	=	function(FRAME, Type)	{
+	UL	=	cbind(FRAME,							Type,	"Sample")
+	UR	=	cbind(FRAME[,1] + 16,	FRAME[,2],		Type,	"Tap")
+	LL	=	cbind(FRAME[,1],		FRAME[,2] - 16,	Type,	"Tap")
+	LR	=	cbind(FRAME[,1] + 16,	FRAME[,2] - 16,	Type,	"Tap")
+
+
+	colnames(UL)	=	NAMES
+	colnames(UR)	=	NAMES
+	colnames(LL)	=	NAMES
+	colnames(LR)	=	NAMES
+	return(rbind(UL, UR, LL, LR))
+}
+
+AXESpd = list(
+	scale_x_continuous(name = NULL, limits = c(-8, 8+16), breaks = -7:(8+16), minor_breaks = NULL, labels = NULL, expand = c(0,0)), 
+	scale_y_continuous(name = NULL, limits = c(-8-16, 8), breaks = (-7-16):8, minor_breaks = NULL, labels = NULL, expand = c(0,0)), 
+	scale_color_manual(guide = "legend", name = "", values = c("Sample" = "red", "Tap" = "cyan"), breaks = c("Sample", "Tap")),
+	theme(legend.position = c(1, 0.95), legend.direction="horizontal", legend.justification = c(1,-1), legend.background = element_rect(NA)),
+	coord_fixed(ratio = 1),
+	theme(axis.ticks = element_blank())
+)
+
+
+PD8x	=	as.data.frame(rbind(
+	c(-7,	1),
+	c(-5,	-5),
+	c(-3,	5),
+	c(-1,	-3),
+	c(1,	3),
+	c(3,	-7),
+	c(5,	-1),
+	c(7,	7)
+)	)
+
+PD16x	=	as.data.frame(rbind(
+	c(-8,	0),
+	c(-7,	8),
+	c(-6,	-4),
+	c(-5,	2),
+	c(-4,	6),
+	c(-3,	-2),
+	c(-2,	-6),
+	c(-1,	3),
+	c(0,	7),
+	c(1,	-1),
+	c(2,	-5),
+	c(3,	5),
+	c(4,	1),
+	c(5,	-3),
+	c(6,	-7),
+	c(7,	4)
+)	)
+
+MSPD	=	rbind(QUADS(PD8x, "8x"), QUADS(PD16x, "16x"))
+
+MSPD		=	FAC2NUM(MSPD, 1:2)
+MSPD[,3]	=	factor(MSPD[,3], levels = ORDERMS, ordered = TRUE)
+
+ggplot(data = MSPD, aes(x = x, y = y)) + 
+ggtitle("DirectX Standard Sample Patterns (Poisson Disk)") + 
+BORD +
+geom_point(data = MSPD[MSPD$Pattern == "8x",],	color = "black",	size = 24,		shape = 1) + 
+geom_point(data = MSPD[MSPD$Pattern == "16x",],	color = "black",	size = 20,	shape = 1) + 
+geom_point(aes(color = Type),	size = 7) + 
+facet_grid(cols = vars(Pattern)) + AXESpd + theme(legend.position = "none")
+
+customSave("Poisson Disks", "both", width = 4/5*16)