LJITColors, there’s a name for that

I have written about curating color data in the past: Curating Data – Resene and Hollasch Colors

Now, here it is, two years later, and I find a reason to revisit the topic.  Really I just wanted to create a new repository on GitHub which isolated my color related stuff because I was finding it hard to find it.  So, I wrote some code, and put it in this LJITColors repository.

What’s there?  Well, first of all, you must have some color databases.  The allcolors.lua file contains color tables for; Crayola, Hollasch, Resene, SGI.  These are just the tables that I’ve curated from around the web that I find to be interesting.  A color table is nothing more than a name/value pair that might look like this:


local CrayolaColors = {
	navyblue = {25, 116, 210},
	seagreen = {159, 226, 191},
	screamingreen = {118, 255, 122},
	greenblue = {17, 100, 180},
	royalpurple = {120, 81, 169},
	bluegray = {102, 153, 204},
	blizzardblue = {172, 229, 238},

And at the end of the allcolors.lua file we find:

return {
	resene = ReseneColors,
	crayola = CrayolaColors,
	hollasch = HollaschColors,
	sgi = SGIColors,

This in and of itself is interesting because right away you can already do something as simple as:

local colordb = require("allcolors")
local screaminggreen = colordb.crayola.screaminggreen

And you’ll get the RGB triplet that represents the ‘screaminggreen’ color. OK, that might be useful for some use cases. But, since you have the data in a form that is easily searchable and maliable, you can do even more.

Let’s say you want to lookup a color based on a fragment of the name. You want some form of green, but you’re not sure what exactly, so you just want to explore. Let’s say you want to know all the colors in the Crayola set that have the word “yellow” in them:

 	local found = colorman.matchColorByName("yellow", colorman.colordb["crayola"], "crayola")

This returns a set of values that looks like:

    {dbname ="Crayola", name="lemmonyellow", color={255,244,79}}

   crayola ultrayellow          255  164  116
   crayola yellowgreen          197  227  132
   crayola lemonyellow          255  244   79
   crayola orangeyellow         248  213  104
   crayola yellow               252  232  131
   crayola yelloworange         255  174   66
   crayola greenyellow          240  232  145
   crayola unmellowyellow       255  255  102

Well, that’s pretty spiffy I think. And if you want to search the whole database, and not just one set, you can use this form:

	local found = getColorLikeName(pattern)

The ‘pattern’ is used in a lua string.find() function, so it can actually be a complex expression if you like.

Although looking up color values by name is useful and interesting, looking up by component values might be even more interesting. This is where things get really interesting though. Let’s imagine we want to lookup colors that appear to be ‘white’ {255, 255, 255}.

My first naïve attempt at doing this was to make the observation that the triplet is just a vector. Well, if I can find the angle between two vectors, then a ‘match’ is simply when two vectors have an angle close to zero. Yah!! That’s the ticket.

local function normalize(A)
	local mag = math.sqrt(A[1]*A[1] + A[2]*A[2] + A[3]*A[3])
	return {A[1]/mag, A[2]/mag, A[3]/mag}

-- linear algebra dot product
local function dot(A,B)
	return A[1]*B[1]+A[2]*B[2]+A[3]*B[3];

local function angleBetweenColors(A, B)
	local a = normalize(A)
	local b = normalize(B)
	local angle = acos(dot(a,b))

	return angle

local function matchColorByValue(color, db, dbname)
	local colors = {}

	for name, candidate in pairs(db) do
		local angle = angleBetweenColors(color, candidate)
		if (angle < 0.05) then
			table.insert(colors, {dbname=dbname, name=name, color = candidate})

	return colors;

Then I can just do the following to find the “white” colors:

	local found = colorman.matchColorByValue({255,255,255}, colorman.colordb.sgi, "sgi")

This results in about 250 entries that look like this:

       sgi seashell1            255  245  238
       sgi gainsboro            220  220  220
       sgi grey20                51   51   51
       sgi oldlace              253  245  230
       sgi grey85               217  217  217
       sgi grey30                77   77   77
       sgi gray73               186  186  186
       sgi grey45               115  115  115
       sgi gray31                79   79   79
       sgi grey51               130  130  130
       sgi gray92               235  235  235
       sgi grey                 190  190  190
       sgi grey38                97   97   97
       sgi grey62               158  158  158
       sgi gray27                69   69   69
       sgi gray39                99   99   99
       sgi grey11                28   28   28

Huh? What’s that about? Well, upon further inspection, it did exactly what I asked. It found all the colors that have the same normalized vector. In that context, there’s no difference between {28, 28, 28} and {255, 255, 255}. Hmmm, so what I need to also take account of is the luminance value, so I get a similar direction and magnitude if you will.

-- Convert to luminance using ITU-R Recommendation BT.709 (CCIR Rec. 709)
-- This is the one that matches modern HDTV and LCD monitors
local function lumaBT709(c)
	local gray = 0.2125 * c[1] + 0.7154 * c[2] + 0.0721 * c[3]

	return gray;

local function matchColorByValue(color, db, dbname)
	local colors = {}
	local colorluma = lumaBT709(color)

	for name, candidate in pairs(db) do
		local angle = angleBetweenColors(color, candidate)
		local candidateluma = lumaBT709(candidate)
		if (angle < 0.05) and (abs(candidateluma - colorluma) < 5) then
			table.insert(colors, {dbname=dbname, name=name, color = candidate})

	return colors;

This time, the set is more like what I was after:

       sgi gray100              255  255  255
       sgi snow1                255  250  250
       sgi azure                240  255  255
       sgi ivory1               255  255  240
       sgi grey99               252  252  252
       sgi gray99               252  252  252
       sgi ivory                255  255  240
       sgi grey100              255  255  255
       sgi mintcream            245  255  250
       sgi floralwhite          255  250  240
       sgi snow                 255  250  250
       sgi honeydew1            240  255  240
       sgi azure1               240  255  255
       sgi honeydew             240  255  240
       sgi white                255  255  255

And, again, if I want to do it over the entire database:

	local found = colorman.getColorByValue({255,255,255})
    resene ricecake             255  254  240
    resene blackwhite           255  254  246
    resene bianca               252  251  243
    resene quarterpearllusta    255  253  244
    resene soapstone            255  251  249
    resene orchidwhite          255  253  243
    resene halfpearllusta       255  252  234
    resene apricotwhite         255  254  236
    resene romance              255  254  253
    resene clearday             233  255  253
    resene whitenectar          252  255  231
    resene butterywhite         255  252  234
    resene promenade            252  255  231
    resene wanwhite             252  255  249
    resene sugarcane            249  255  246
    resene hintofyellow         250  253  228
    resene seafog               252  255  249
    resene rocksalt             255  255  255
    resene travertine           255  253  232
    resene ceramic              252  255  249
    resene alabaster            255  255  255
    resene chileanheath         255  253  230
    resene dew                  234  255  254
    resene bridalheath          255  250  244
    resene hintofgrey           252  255  249
    resene islandspice          255  252  238
    resene chinaivory           252  255  231
    resene orangewhite          254  252  237
   crayola white                255  255  255
  hollasch azure                240  255  255
  hollasch snow                 255  250  250
  hollasch ivory                255  255  240
  hollasch titanium_white       252  255  240
  hollasch mint_cream           245  255  250
  hollasch floral_white         255  250  240
  hollasch white                255  255  255
  hollasch honeydew             240  255  240
       sgi gray100              255  255  255
       sgi snow1                255  250  250
       sgi azure                240  255  255
       sgi ivory1               255  255  240
       sgi grey99               252  252  252
       sgi gray99               252  252  252
       sgi ivory                255  255  240
       sgi grey100              255  255  255
       sgi mintcream            245  255  250
       sgi floralwhite          255  250  240
       sgi snow                 255  250  250
       sgi honeydew1            240  255  240
       sgi azure1               240  255  255
       sgi honeydew             240  255  240
       sgi white                255  255  255

Now we’re cooking with gas!

So, originally, I was interested in curating a few sets of colors just so that I’d always have some color sets readily available. Now, I’ve turned those color sets into a quick and dirty database, and thrown in some data set specific search routines which makes them much more useful. For color matching, I can imagine picking up a few pixels from a bitmap image, and doing color matching to find ways to blend and extend.

It’s all fun, and realizations like taking into account the luminance value, makes the learning that much more interesting.

So, there you have it.

Drawing Curvy Lines with aplomb – Beziers

I have written plenty about Bezier and other curves and surfaces.  That was largely in the context of 3D printing using OpenScad, or BanateCad.  But now, I’m adding to a general low level graphics library.


Well well, what do we have here.  Bezier curves are one of those constructs where you lay down some ‘control points’ and then draw a line that meanders between them according to some mathematical formula.  In the picture, the green curve is represented by 4 control points, the red one is represented by 5 points, and the blue ones are each represented by 4 points.

How do you construct a Bezier curve?  Well, you don’t need much more than the following code:

void computeCoefficients(const int n, int * c)
	int k, i;

	for (k = 0; k <= n; k++)
		// compute n!/(k!(n-k)!)
		c[k] = 1;
		for (i = n; i >= k + 1; i--)
			c[k] *= i;

		for (i = n - k; i >= 2; i--)
			c[k] /= i;

void computePoint(const float u, Pt3 * pt, const int nControls, const Pt3 *controls, const int * c)
	int k;
	int n = nControls - 1;
	float blend;

	pt->x = 0.0;	// x
	pt->y = 0.0;	// y
	pt->z = 0.0;	// z
	// Add in influence of each control point
	for (k = 0; k < nControls; k++){
		blend = c[k] * powf(u, k) *powf(1 - u, n - k);
		pt->x += controls[k].x * blend;
		pt->y += controls[k].y * blend;
		pt->z += controls[k].z * blend;

void bezier(const Pt3 *controls, const int nControls, const int m, Pt3 * curve)
	// create space for the coefficients
	int * c = (int *)malloc(nControls * sizeof(int));
	int i;

	computeCoefficients(nControls - 1, c);
	for (i = 0; i <= m; i++) {
		computePoint(i / (float)m, &curve[i], nControls, controls, c);

This is pretty much the same code you would get from any book or tutorial on fundamental computer graphics. It will allow you to calculate a Bezier curve using any number of control points.

Here’s the test case that generated the picture

typedef struct {
	REAL x;
	REAL y;
	REAL z;
} Pt3;

void polyline(pb_rgba *pb, Pt3 *curve, const int nPts, int color)
	for (int idx = 0; idx < nPts; idx++) {
		raster_rgba_line(pb, curve[idx].x, curve[idx].y, curve[idx + 1].x, curve[idx + 1].y, color);

void test_bezier()

	size_t width = 400;
	size_t height = 400;
	int centerx = width / 2;
	int centery = height / 2;
	int xsize = (int)(centerx*0.9);
	int ysize = (int)(centery*0.9);

	pb_rgba pb;
	pb_rgba_init(&pb, width, height);

	// background color
	raster_rgba_rect_fill(&pb, 0, 0, width, height, pLightGray);

	// One curve drooping down
	Pt3 controls[4] = { { centerx - xsize, centery, 0 }, { centerx, centery + ysize, 0 }, { centerx, centery + ysize, 0 }, { centerx + xsize, centery, 0 } };
	int nControls = 4;
	int m = 60;
	Pt3 curve[100];
	bezier(controls, nControls, m, curve);
	polyline(&pb, curve, m, pGreen);

	// Several curves going up
	for (int offset = 0; offset < ysize; offset += 5) {
		Pt3 ctrls2[4] = { { centerx - xsize, centery, 0 }, { centerx, centery - offset, 0 }, { centerx, centery - offset, 0 }, { centerx + xsize, centery, 0 } };
		bezier(ctrls2, nControls, m, curve);
		polyline(&pb, curve, m, pBlue);

	// one double peak through the middle
	Pt3 ctrls3[5] = { { centerx - xsize, centery, 0 }, { centerx-(xsize*0.3f), centery + ysize, 0 }, { centerx, centery - ysize, 0 }, { centerx+(xsize*0.3f), centery + ysize, 0 }, { centerx + xsize, centery, 0 } };
	int nctrls = 5;
	bezier(ctrls3, nctrls, m, curve);
	polyline(&pb, curve, m, pRed);

	// Now we have a simple image, so write it to a file
	int err = write_PPM("test_bezier.ppm", &pb);

From here, there are some interesting considerations. For example, you don’t want to calculate the coefficients every single time you draw a single curve. In terms of computer graphics, most Bezier curves consist of 3 or 4 points at most. Ideally, you would calculate the coefficients for those specific curves and store the values statically for later usage. This is what you’d do ideally for a small embedded library. The tradeoff in storage space is well worth the savings in compute time.

Additionally, instead of calculating all the line segments and then storing those values and using a polyline routine to draw things, you’d like want to simply have the bezier routine draw the lines directly. That would cut down on temporary allocations.

At the same time though, you want to retain the ‘computePoint’ function as independent because once you have a Bezier calculation function within the library, you’ll want to use it to do things other than just draw curved lines. Bezier, and it’s corollary Hermite, are good for calculating things like color ramps, motion, and other curvy stuff. This is all of course before you start using splines and nurbs, which are much more involved process.

There you have it, a couple of functions, and suddenly you have Bezier curves based on nothing more than the low level line drawing primitives. At the moment, this code sits in a test file, but soon enough I’ll move it into the graphicc library proper.

GraphicC – The triangle’s the thing

Pixels, lines, and squares, oh my!

And, finally, we come to triangles.  The demo code is thus:

#include "test_common.h"

void test_writebitmap()
	size_t width = 480;
	size_t height = 480;
	pb_rgba pb;
	pb_rgba_init(&pb, width, height);

	// Draw some triangles 
	size_t midx = (size_t)(width / 2);
	size_t midy = (size_t)(height / 2);

	raster_rgba_triangle_fill(&pb, 0, 0, width-1, 0, midx, midy, pRed);
	raster_rgba_triangle_fill(&pb, 0, 0, midx, midy, 0, height-1, pGreen);
	raster_rgba_triangle_fill(&pb, width-1, 0, midx, midy, width-1, height - 1, pBlue);
	raster_rgba_triangle_fill(&pb, midx, midy, 0, height-1, width - 1, height - 1, pDarkGray);

	// Now we have a simple image, so write it to a file
	int err = write_PPM("test_triangle.ppm", &pb);

int main(int argc, char **argv)

	return 0;

Why triangles? Well, beyond pixels, and lines, they are one of the most useful drawing primitives. When it finally comes to rendering in 3D for example, it will all be about triangles. Graphics hardware over the years has been optimized to render triangles as well, so it is beneficial to focus more attention to this primitive than to any other. You might think polygons are very useful, but, all polygons can be broken down into triangles, and we’re back where we started.

Here’s the triangle drawing routine:

#define swap16(a, b) { int16_t t = a; a = b; b = t; }

typedef struct _point2d
	int x;
	int y;
} point2d;

int FindTopmostPolyVertex(const point2d *poly, const size_t nelems)
	int ymin = INT32_MAX;
	int vmin = 0;

	size_t idx = 0;
	while (idx < nelems) {
		if (poly[idx].y < ymin) {
			ymin = poly[idx].y;
			vmin = idx;

	return vmin;

void RotateVertices(point2d *res, point2d *poly, const size_t nelems, const int starting)
	size_t offset = starting;
	size_t idx = 0;
	while (idx < nelems) {
		res[idx].x = poly[offset].x;
		res[idx].y = poly[offset].y;
		if (offset > nelems-1) {
			offset = 0;


void sortTriangle(point2d *sorted, const int x1, const int y1, const int x2, const int y2, const int x3, const int y3)
	point2d verts[3] = { { x1, y1 }, { x2, y2 }, { x3, y3 } };

	int topmost = FindTopmostPolyVertex(verts, 3);
	RotateVertices(sorted, verts, 3, topmost);

void raster_rgba_triangle_fill(pb_rgba *pb, 
	const unsigned int x1, const unsigned int  y1, 
	const unsigned int  x2, const unsigned int  y2, 
	const unsigned int  x3, const unsigned int  y3, 
	int color)
	int a, b, y, last;

	// sort vertices, such that 0 == y with lowest number (top)
	point2d sorted[3];
	sortTriangle(sorted, x1, y1, x2, y2, x3, y3);

	// Handle the case where points are colinear (all on same line)
	if (sorted[0].y == sorted[2].y) { 
		a = b = sorted[0].x;
		if (sorted[1].x < a) 
			a = sorted[1].x;
		else if (sorted[1].x > b) 
			b = sorted[1].x;

		if (sorted[2].x < a) 
			a = sorted[2].x;
		else if (sorted[2].x > b) 
			b = sorted[2].x;

		raster_rgba_hline(pb, a, sorted[0].y, b - a + 1, color);

		dx01 = sorted[1].x - sorted[0].x,
		dy01 = sorted[1].y - sorted[0].y,
		dx02 = sorted[2].x - sorted[0].x,
		dy02 = sorted[2].y - sorted[0].y,
		dx12 = sorted[2].x - sorted[1].x,
		dy12 = sorted[2].y - sorted[1].y;
	int32_t sa = 0, sb = 0;

	// For upper part of triangle, find scanline crossings for segments
	// 0-1 and 0-2. If y1=y2 (flat-bottomed triangle), the scanline y1
	// is included here (and second loop will be skipped, avoiding a /0
	// error there), otherwise scanline y1 is skipped here and handled
	// in the second loop...which also avoids a /0 error here if y0=y1
	// (flat-topped triangle).
	if (sorted[1].y == sorted[2].y) 
		last = sorted[1].y; // Include y1 scanline
		last = sorted[1].y - 1; // Skip it
	for (y = sorted[0].y; y <= last; y++) 
		a = sorted[0].x + sa / dy01;
		b = sorted[0].x + sb / dy02;
		sa += dx01;
		sb += dx02;
		/* longhand:
		a = x0 + (x1 - x0) * (y - y0) / (y1 - y0);
		b = x0 + (x2 - x0) * (y - y0) / (y2 - y0);
		if (a > b) swap16(a, b);
		raster_rgba_hline(pb, a, y, b - a + 1, color);

	// For lower part of triangle, find scanline crossings for segments
	// 0-2 and 1-2. This loop is skipped if y1=y2.
	sa = dx12 * (y - sorted[1].y);
	sb = dx02 * (y - sorted[0].y);
	for (; y <= sorted[2].y; y++) 
		a = sorted[1].x + sa / dy12;
		b = sorted[0].x + sb / dy02;
		sa += dx12;
		sb += dx02;
		/* longhand:
		a = x1 + (x2 - x1) * (y - y1) / (y2 - y1);
		b = x0 + (x2 - x0) * (y - y0) / (y2 - y0);
		if (a > b) 
			swap16(a, b);

		raster_rgba_hline(pb, a, y, b - a + 1, color);

This seems like a lot of work to simply draw a triangle! There are lots of routines for doing this. This particular implementation borrows from a couple of different techniques. The basic idea is to first sort the vertices in scaline order, top to bottom. That is, we want to known which vertex to start from because we’re going to follow an edge down the framebuffer, drawing lines between edges as we go. In a regular triangle, without a flat top or bottom, there will be a switch between driving edges as we encounter the third point somewhere down the scan lines.

At the end, the ‘raster_rgba_hline’ function is called to actually draw a single line. If we wanted to do blending, we’d change this line. If we wanted to use a color per vertex, it would ultimately be dealt with here. All possible. Not necessary for the basic routine. With some refactoring, this could be made more general purpose, and different rendering modes could be included.

This is the only case where I use a data structure, to store the sorted points. Most of the time I just pass parameters and pointers to parameters around.

This is also a good time to mention API conventions. One of the constraints from the beginning is the need to stick with basic C constructs, and not get too fancy. In some cases this is at the expense of readability, but in general things just work out ok, as it’s simple to get used to. So, let’s look at the API here:

void raster_rgba_triangle_fill(pb_rgba *pb, 
	const unsigned int x1, const unsigned int  y1, 
	const unsigned int  x2, const unsigned int  y2, 
	const unsigned int  x3, const unsigned int  y3, 
	int color)

That’s a total of 8 parameters. If I were going for absolute speed, and I knew the platform I was running on, I might try to limit the parameters to 4, to help ensure they get passed in registers, rather than requiring the use of a stack. But, that’s an optimization that’s iffy at best, so I don’t bother. And why not use some data structures? Clearly x1, y1 is a 2D point, so why not use a ‘point’ data structure. Surely where the data comes from is structured as well. In some cases it is, and in others it is not. I figure that in the cases where the data did come from a structure, it’s fairly easy for the caller to do the dereferencing and pass in the values directly. In the cases where the data did not come from a point structure, it’s a tax to pay to stuff the data into a point structure, simply to have it pass in to a function, which may not need it in that form. So, in general, all the parameters are passed in a ‘denormalized’ form. With small numbers of easy to remember parameters, I think this is fine.

Also, I did decide that it was useful to use ‘const’ in most cases where that is applicable.  This gives the compiler some hints as to how best deal with the parameters, and allows you to specify constants inline for test cases, without compiler complaints.

There is a decided lack of error handling in most of these low level APIs.  You might think that triangle drawing would be an exception.  Shouldn’t I do some basic clipping to the framebuffer?  The answer is no, not at this level.  At a higher level, we might be drawing something larger, where a triangle is but a small part.  At that higher level we’ll know about our framebuffer, or other constraints that might cause clipping of a triangle.  At that level, we can perform the clipping, and send down new sets of triangles to be rendered by this very low level triangle drawing routine.

Of course, this routine could be made even more raw and optimized by breaking out the vertex sorting from the edge following part.  If the triangle vertices don’t change, there’s no need to sort them every time they are drawn, so making the assumption that the vertices are already in framebuffer height order can dramatically simplify the drawing portion.  Then, the consumer can call the sorting routines when they need to, and pass in the sorted vertex values.

And thus APIs evolve.  I’ll wait a little longer before making such changes as I might think of other things that I want to improve along the way.

There you have it then.  From pixels to triangles, the basic framebuffer drawing routines are now complete.  What more could be needed at this level?  Well, dealing with some curvy stuff, like ellipses and rounded rectangles might be nice, all depends on what use cases are more interesting first, drawing pies and graphs, or doing some UI stuff.  The first thing I want to do is display some data related to network traffic events, so I think I’ll focus on a little bit of text rendering first, and leave the ellipse and rounded rects for later.

So, next time around, doing simple bitmap text.

GraphicC – Random Lines

Thus far, I’ve been able to draw individual pixels, some rectangles, straight vertical and horizontal lines.  Now it’s time to tackle those lines that have an arbitrary slope.


In this case, we’re only interested in the line drawing, not the rectangles and triangles.  Here’s the example code:


#include &quot;test_common.h&quot;

void test_writebitmap()
	size_t width = 480;
	size_t height = 480;
	pb_rgba pb;
	pb_rgba_init(&amp;pb, width, height);

	// draw horizontal lines top and bottom
	raster_rgba_hline(&amp;pb, 0, 0, width - 1, pWhite);
	raster_rgba_hline(&amp;pb, 0, height - 1, width - 1, pWhite);

	// draw vertical lines left and right
	raster_rgba_vline(&amp;pb, 0, 0, height - 1, pGreen);
	raster_rgba_vline(&amp;pb, width - 1, 0, height - 1, pTurquoise);

	// draw criss cross lines
	raster_rgba_line(&amp;pb, 0, 0, width - 1, height - 1, pRed);
	raster_rgba_line(&amp;pb, width - 1, 0, 0, height - 1, pYellow);

	// draw a couple of rectangles
	raster_rgba_rect_fill(&amp;pb, 5, 5, 60, 60, pLightGray);
	raster_rgba_rect_fill(&amp;pb, width - 65, height - 65, 60, 60, pLightGray);

	// draw a rectangle in the center
	pb_rgba fpb;
	pb_rgba_get_frame(&amp;pb, (width / 2) - 100, (height / 2) - 100, 200, 200, &amp;fpb);
	raster_rgba_rect_fill(&amp;fpb, 0, 0, 200, 200, pBlue);

	// Draw triangle 
	raster_rgba_triangle_fill(&amp;pb, 0, height - 10, 0, 10, (width / 2) - 10, height / 2, pGreen);

	// Now we have a simple image, so write it to a file
	int err = write_PPM(&quot;test_writebitmap.ppm&quot;, &amp;pb);


int main(int argc, char **argv)

	return 0;

This is the part we’re interested in here:

	// draw criss cross lines
	raster_rgba_line(&amp;pb, 0, 0, width - 1, height - 1, pRed);
	raster_rgba_line(&amp;pb, width - 1, 0, 0, height - 1, pYellow);

Basically, feed in x1, y1, x2, y2 and a color, and a line will be drawn. The operation is SRCCOPY, meaning, the color is not blended, it just lays over whatever is already there. And the line drawing routine itself?

#define sgn(val) ((0 &lt; val) - (val &lt; 0))

// Bresenham simple line drawing
void raster_rgba_line(pb_rgba *pb, unsigned int x1, unsigned int y1, unsigned int x2, unsigned int y2, int color)
	int dx, dy;
	int i;
	int sdx, sdy, dxabs, dyabs;
	unsigned int x, y, px, py;

	dx = x2 - x1;      /* the horizontal distance of the line */
	dy = y2 - y1;      /* the vertical distance of the line */
	dxabs = abs(dx);
	dyabs = abs(dy);
	sdx = sgn(dx);
	sdy = sgn(dy);
	x = dyabs &gt;&gt; 1;
	y = dxabs &gt;&gt; 1;
	px = x1;
	py = y1;

	pb_rgba_set_pixel(pb, x1, y1, color);

	if (dxabs &gt;= dyabs) /* the line is more horizontal than vertical */
		for (i = 0; i&lt;dxabs; i++)
			y += dyabs;
			if (y &gt;= (unsigned int)dxabs)
				y -= dxabs;
				py += sdy;
			px += sdx;
			pb_rgba_set_pixel(pb, px, py, color);
	else /* the line is more vertical than horizontal */
		for (i = 0; i&lt;dyabs; i++)
			x += dxabs;
			if (x &gt;= (unsigned int)dyabs)
				x -= dyabs;
				px += sdx;
			py += sdy;
			pb_rgba_set_pixel(pb, px, py, color);

This is a fairly simple implementation of the well known Bresenham line drawing algorithm. It may no longer be the fastest in the world, but it’s fairly effective and compoutationally simple. If we wanted to do a blend of colors, then the ‘pb_rgba_set_pixel’ could simple be replaced with the blending routine that we saw in the other line drawing routines.

And that’s that. You could implement this as EFLA, or any number of other routines that might prove to be faster. But, why optimize too early? It might be that memory access is the bottleneck, and not the simple calculations done here. Bresenham is also fairly nice because everything is simple integer arithmetic, which is both fairly fast, as well as easy to implement on an FPGA, if it comes to that. Certainly on a microcontroller, it would be preferred to float/double.

Why we’re at it, how about that bitmap writing to file routine?

	int err = write_PPM(&quot;test_writebitmap.ppm&quot;, &amp;pb);

I’ve seen plenty of libraries that spend an inordinate amount of lines of code on the simple image load/save portion of things. That can easily dominate anything else you do. I didn’t want to really pollute the basic codebase with all that, so I chose the ‘ppm’ format as the only format that the library speaks natively. It’s a good ol’ format, nothing fancy, basic RGB dump of values, with some text at the beginning to describe the format of the image. The routine looks like this:


#pragma once

#ifndef PBM_H
#define PBM_H

#include &quot;pixelbuffer.h&quot;

#ifdef __cplusplus
extern &quot;C&quot; {

int write_PPM(const char *filename, pb_rgba *fb);

#ifdef __cplusplus



#include "pbm.h"


#pragma warning(push)
#pragma warning(disable: 4996)	// _CRT_SECURE_NO_WARNINGS (fopen) 

int write_PPM(const char *filename, pb_rgba *fb)
	FILE * fp = fopen(filename, "wb");
	if (!fp) return -1;

	// write out the image header
	fprintf(fp, "P6\n%d %d\n255\n", fb-&gt;frame.width, fb-&gt;frame.height);
	// write the individual pixel values in binary form
	unsigned int * pixelPtr = (unsigned int *)fb-&gt;data;

	for (size_t row = 0; row frame.height; row++) {
		for (size_t col = 0; col frame.width; col++){
			fwrite(&amp;pixelPtr[col], 3, 1, fp);
		pixelPtr += fb-&gt;pixelpitch;


	return 0;

#pragma warning(pop)

There are lots of different ways to do this, but basically, get a pointer to the pixel values, and write out the RGB portion (ignoring the Alpha portion). The first line written is in plaintext, and it tells the format ‘P6’, followed by the width and height of the image. And that’s that. The internal format of a framebuffer is fairly simple, so writing a whole library that can read and write things like GIF, PNG, JPG and the like can be done fairly easily, and independently of the core library. And that’s probably the best way to do it. Then the consumer of this library isn’t forced to carry along complexity they don’t need, but they can simply compose what is necessary for their needs.

Alright then. There is one more primitive, the triangle, which will complete the basics of the drawing routines. So, next time.

GraphicC – Who’s line is it?


After pixels, drawing lines are probably the next most useful primitive in a graphics system.  Perhaps bitblt is THE most useful, but lines are certain up there.  There are a few things going on in the picture above, so I’m going to go through them bit by bit.

This is the code that does it:

#include "test_common.h"

void test_linespan()
	size_t width = 320;
	size_t height = 240;
	pb_rgba pb;
	pb_rgba_init(&pb, width, height);

	// Set a white background
	raster_rgba_rect_fill(&pb, 0, 0, width, height, pWhite);

	// do a horizontal fade
	int color1 = RGBA(127, 102, 0, 255);
	int color2 = RGBA(0, 127, 212, 255);

	for (size_t row = 0; row < 100; row++) {
		int x1 = 0;
		int x2 = width - 1;
		raster_rgba_hline_span(&pb, x1, color1, x2, color2, row);

	// Draw a button looking thing
	// black
	raster_rgba_hline(&pb, 20, 20, 80, pBlack);
	raster_rgba_hline(&pb, 20, 21, 80, pDarkGray);
	raster_rgba_hline(&pb, 20, 22, 80, pLightGray);

	// light gray rect
	raster_rgba_rect_fill(&pb, 20, 23, 80, 24, pLightGray);

	// fade to black
	for (size_t col = 20; col < 100; col++) {
		raster_rgba_vline_span(&pb, 46, pLightGray, 77, pBlack, col);

	// Draw some blended lines atop the whole
	for (size_t row = 35; row < 120; row++){
		raster_rgba_hline_blend(&pb, 45, row, 100, RGBA(0, 153, 153, 203));

	// Now we have a simple image, so write it to a file
	int err = write_PPM("test_linespan.ppm", &pb);


int main(int argc, char **argv)

	return 0;

In most graphics systems, there are three kinds of lines;

  • horizontal
  • vertical
  • sloped

Along with the kind of line, there are typically various attributes such as thickness, color,
and in the case of joined lines, what kind of joinery (butted, mitered, rounded).

At the various lowest level though, there are simply lines, and the things I focus on are slopes and colors.

There are two basic lines kinds that are of particular interest right off the bat, those are horizontal and vertical.  They are special cases because their drawing can be easily optimized, and if you have any acceleration hardware, these are most likely included.  This kinds of brings up another design desire.

  • Can be implemented in an fpga

But, that’s for a much later time.  For now, how about those horizontal and vertical lines?
If what you want is a solid line, of a single color, ignoring any transparency, then you want a simple hline:

int raster_rgba_hline(pb_rgba *pb, unsigned int x, unsigned int y, unsigned int length, int value)
	size_t terminus = x + length;
	x = x < 0 ? 0 : x;
	terminus = terminus - x;

	unsigned int * data = &((unsigned int *)pb->data)[y*pb->pixelpitch+x];
	size_t count = 1;
	for (size_t idx = 0; idx < terminus; idx++)
		*data = value;

	return 0;

This makes a simple rectangle easy to implement as well:

#define raster_rgba_rect_fill(pb, x1, y1, width, height, value) for (size_t idx = 0; idx < height; idx++){raster_rgba_hline(pb, x1, y1 + idx, width, value);	}

Simple single color horizontal lines can be drawn quickly, often times using some form of memset
on the host platform. Even in the case where a tight inner loop is used, what appears to be
fairly slow can be quite fast depending on how your compiler optimizes things.

There is a corresponding ‘vline’ routine that does similar.

int raster_rgba_vline(pb_rgba *pb, unsigned int x, unsigned int y, unsigned int length, int value)
    unsigned int * data = &((unsigned int *)pb->data)[y*pb->frame.width + x];
    size_t count = 1;
    while (count <= length) {
        *data = value;
        data += pb->pixelpitch;

    return 0;

Here, the same basic assignment is used, after determining the starting offset of the first
pixel. The pointer is advanced by the pixelpitch, which in this case is the count of 32-bit
integer values per row. If you’re rendering into a framebuffer that doesn’t conform to this,
then this offset can be adjusted accordingly.

Horizontal and vertical lines of a solid color are nice, and can go a long way towards satisfying
some very basic drawing needs. But, soon enough you’ll want those lines to do a little bit more
work for you.

void raster_rgba_hline_span(pb_rgba *pb, int x1, int color1, int x2, int color2, int y)
    int xdiff = x2 - x1;
    if (xdiff == 0)

    int c1rd = GET_R(color1);
    int c1gr = GET_G(color1);
    int c1bl = GET_B(color1);

    int c2rd = GET_R(color2);
    int c2gr = GET_G(color2);
    int c2bl = GET_B(color2);

    int rdx = c2rd - c1rd;
    int gdx = c2gr - c1gr;
    int bdx = c2bl - c1bl;

    float factor = 0.0f;
    float factorStep = 1.0f / (float)xdiff;

    // draw each pixel in the span
    for (int x = x1; x < x2; x++) {
        int rd = c1rd + (int)(rdx*factor);
        int gr = c1gr + (int)(gdx*factor);
        int bl = c1bl + (int)(bdx*factor);
        int fg = RGBA(rd, gr, bl, 255);
        pb_rgba_set_pixel(pb, x, y, fg);

        factor += factorStep;

Let’s imagine you want to draw that fade from green to blue. You could do it pixel by pixel,
but it’s nice to have a simple line drawing routine that does it for you.

The ‘raster_rgba_hline_span’ routine takes two colors, as well as the x1, x2, and y values. It
will draw a horizontal line between x1 and x2 (inclusive), going from color1, to color2 in a
linear fashion. Same goes for the corresponding vline_span routine. This is nice and simple.
You could modify it a bit to change the parameters that are passed in, and fuss with trying to
optimize the loop in various ways, but this basically works.

Great, we have solid lines, line spans with color fading, what about transparency?

The individual pixels are represented with 32-bits each. There are 8-bits each for R, G, and B
color components. The ‘A’ portion of the color is not used by the frame buffer, but rather used
to represent an opacity value. The opacity just determines how much of the color will be shown
if this color is blended with another color.

In the picture above, the turquoise rectangle is blended with the pixels that are below, rather
than just copying its pixels atop the others.

In order to do that, we want to draw some horizontal lines, but we want to blend the colors
instead of copy them:

// Draw some blended lines atop the whole
for (size_t row = 35; row < 120; row++)
    raster_rgba_hline_blend(&pb, 45, row, 100, RGBA(0, 153, 153, 203));

The ‘raster_rgba_hline_blend’ routine does the needful. It takes a color with an alpha (opacity)
value of 203, and blends that with whatever is already in the specified frame buffer. It looks
like this:

#define blender(bg, fg, a) ((uint8_t)((fg*a+bg*(255-a)) / 255))

#define blend_color(bg, fg) RGBA(                \
    blender(GET_R(bg), GET_R(fg), GET_A(fg)),    \
    blender(GET_G(bg), GET_G(fg), GET_A(fg)),    \
    blender(GET_B(bg), GET_B(fg), GET_A(fg)),    255)

int raster_rgba_hline_blend(pb_rgba *pb, unsigned int x, unsigned int y, unsigned int length, int value)
    size_t terminus = x + length;
    x = x < 0 ? 0 : x;
    terminus = terminus - x;

    unsigned int * data = &((unsigned int *)pb->data)[y*pb->pixelpitch + x];
    size_t count = 1;
    for (size_t idx = 0; idx < terminus; idx++)
        int bg = *data;
        int fg = value;

        *data = blend_color(bg, fg);

    return 0;

The use of macros here keeps the operations straight, and provides easy routines that can be used elsewhere.
It’s a pretty straight forward process though. Each time through the inner loop, the ‘bg’
represents the ‘background’ color, which is taken from the pixel buffer. The ‘fg’ value
represents the color that the user passed in. The new value is a blend of the two, using
the alpha component of the foreground color.

This is a fairly basic routine that can be adapted in many ways. For example, instead of
using the alpha value from the foreground color, you could just pass in a fixed alpha value
to be applied. This is useful when doing something like a ‘fade to black’, without having to
alter each of the source colors directly.

This particular routine only works with solid colors. As such, it is just like the plain
hline routine. So why not have a flag on the hline routine that says to do a blend or not?
Better still, why not have a parameter which is an operation to perform between the bg and fg
pixel values? This is how a lot of libraries work, including good ol’ GDI. I think that overly
complicates matters though. Creating a general purpose routine will introduce a giant switch
statement, or a bunch of function pointers, or something else unworldly. For now, I know I need
only two operators, SRCOPY, SRCOVER, and that’s it, I don’t currently find need for more exotic
operators. But of course, anything can be built atop or easily changed, so who knows.

And that’s about it for the first two kinds of line drawing routines. The third kind, where the
slope is neither vertical nor horizontal, is a little more work, and thus will be saved for
another time.

Woot! Raise the roof up, horizontal and vertical lines, along with pixel copying. What more
could you possibly expect from a basic low level graphics system? Well, for the longest time,
not much more than this, but there’s still some modern conveniences to discuss, such as those
sloped lines, and some more primitives such as triangles.

GraphicC – The Basics

There is one more design constraint I did not mention last time, and it’s a fairly important one for my purposes.

  • Must be easily interfaced from scripting environments

In my particular case, I’m going to favor LuaJIT and its FFI mechanism, and JavaScript, in the form of node.js.  At the very least, this means that I should not utilize too many fancy features, such as classes, operator or function overloading, templates, and the like.  These things are just nasty to deal with from script, and not really worth the benefits in such a small system.  Sticking to C89, or C99 style conventions, at least for the parts that are intended to be publicly accessible, is a good idea.

With that, how about looking at some of the basics.  First up, the most basic thing is the representation of a pixel.  For me, there is a very clear separation between a pixel and a color.  A pixel is a machine representation of a color value.  It is typically in a form that the graphics card can render directly.  Modern day representations are typically RGBA, or RGB, or BGR, BGRA.  That is, one value between 0-255 for each of the color components.  These values are arranged one way or the other, but these are the most typical.  Of course with most modern graphics cards, and leveraging an API such as OpenGL or DirectX, your pixel values can be floats, and laid out in many other forms.  But, I’ll ignore those for now.

Pixel values are constrained in a way, because they are represented by a limited set of byte values.  Colors are a completely different animal.  Then you get into various color spaces such as Cie, or XYZ, or HSL.  They all have their uses depending on the application space you’re in.  In the end though, when you want to display something, you’ve got to convert from those various color spaces to the RGB pixel values that this graphics system can support.

Since I am dealing with pixel values (and not colors), the very lowest level routines deal with pixel buffers, or pixel frames.  That is an array of pixel values.  Simple as that.

typedef struct _pix_rgba {
	unsigned char r, g, b, a;
} pix_rgba;

// On a little endian machine
// Stuff it such that 
// byte 0 == red
// byte 1 == green
// byte 2 == blue
// byte 3 == alpha
#define RGBA(r,g,b,a) ((unsigned int)(a<<24|b<<16|g<<8|r))
#define GET_R(value) ((unsigned int)value &0xff)
#define GET_G(value) (((unsigned int)value &0xff00) >> 8)
#define GET_B(value) (((unsigned int)value &0xff0000) >> 16)
#define GET_A(value) (((unsigned int)value &0xff000000) >> 24)

// pixel buffer rectangle
typedef struct _pb_rect {
	unsigned int x, y, width, height;
} pb_rect;

typedef struct _pb_rgba {
	unsigned char *		data;
	unsigned int		pixelpitch;
	int					owndata;
	pb_rect				frame;
} pb_rgba;

The ‘pb-rgba’ structure is the base of the drawing system. This is the drawing ‘surface’ if you will. It is akin to the ‘framebuffer’ if you were doing graphics in hardware. Things can only be a certain way. The buffer has a known width, height, and number of bytes per row. So far there is only one defined pixel buffer rectangle type, and that supports the rgba layout. I could create different pixel buffer types for different pixel layouts, such as rgba16, or rgb15, or bitmap. But, I don’t need those right now, so this is the only one.

I debated a long time whether the ‘pix_rgba’ structure was needed or not. As you can see from the macros ‘RGBA’ and friends, you can easily stuff the rgba values into an int32. This is good and bad, depending. The truth is, having both forms is useful depending on what you’re doing. If there are machine instructions to manipulate bytes in parallel, one form or the other might be more beneficial. This will be put to the test in blending functions later.

So, what are the most basic functions of this most basic structure?

#ifdef __cplusplus
extern "C" {

int pb_rgba_init(pb_rgba *pb, const unsigned int width, const unsigned int height);
int pb_rgba_free(pb_rgba *pb);

int pb_rgba_get_frame(pb_rgba *pb, const unsigned int x, const unsigned int y, const unsigned int width, const unsigned int height, pb_rgba *pf);

#ifdef __cplusplus

#define pb_rgba_get_pixel(pb, x, y, value) *value = ((unsigned int *)(pb)->data)[(y*(pb)->pixelpitch)+x]
#define pb_rgba_set_pixel(pb, x, y, value) ((unsigned int *)(pb)->data)[(y*(pb)->pixelpitch)+x] = value

#define pb_rect_contains(rect, x, y) ((x>=(rect)->x && x<= (rect)->x+(rect)->width) && ((y>=(rect)->y) && (y<=(rect)->y+(rect)->height)))
#define pb_rect_clear(rect) memset((rect), 0, sizeof(pb_rect))

The ‘pb_rgba_init’ function is the beginning. It will fill in the various fields of the structure, and most importantly allocate memory for storing the actual pixel values. This is very important. Without this, the data pointer points to nothing, or some random part of memory (badness). The corresponding ‘pb_rgba_free’ cleans things up.

The ‘pb_rgba_get_frame’ function copies a portion of a pixel array into another pixel array. You could consider this to be a ‘blit’ function in most libraries. There’s a bit of a twist here though. Instead of actually copying the data, the data pointer is set, and the fields of the receiving frame are set, and that’s it. Why? Because there are many cases where you want to move something around, without having to create multiple copies. Just think of a simple ‘sprite’ based game where you copy some fixed image to multiple places on the screen. You don’t want to have to make multiple copies to do it, just reference some part of a fixed pixel buffer, and do what you will.

Then there are the two macros ‘pb_rgba_get_pixel’, and ‘pb_rgba_set_pixel’. These will get and set a pixel value. Once you have these in hand, you have the keys to the graphics drawing kingdom. Everything else in the system can be based on these two functions. Something as simple as line drawing might use these. There may be optimizations in cases such as horizontal line drawing, but for the most part, this is all you need to write textbook perfect drawing routines.

And that pretty much rounds out the basics up to pixel setting.

It’s kind of amazing to me. Even before really getting into anything interesting, I’ve had to make decisions about some very basic data structure representations, and there are various hidden assumptions as well. For example, there is an hidden assumption that all parameters to the set/get pixel routines are bounds checked. The routines themselves will not perform any bounds checking. This is nice for a composable system, because the consumer can decide where they want to pay for such checking. Doing it per pixel might not be the best place.

There are assumptions about the endianness of the int32 value on the machine, as well as various other large and small assumptions in terms of interfacing to routines (using macros?). There are even assumptions about what the coordinate system is (cartesian), and how it is oriented (top left is 0,0). Of course all of these assumptions must be clearly documented (preferably in the code itself), to minimize the surprises as the system is built and used.

This is a good start though. Here’s how we could use what’s there so far.

#include "test_common.h"

void test_blit()
	size_t width = 640;
	size_t height = 480;

	pb_rgba pb;
	pb_rgba_init(&pb, width, height);

	pb_rgba fpb;
	pb_rgba_get_frame(&pb, 0, 0, width / 2, height / 2, &fpb);

	// draw into primary pixel buffer
	raster_rgba_rect_fill(&pb, 10, 10, (width / 2) - 20, (height / 2) - 20, pBlue);

	// draw the frame in another location
	raster_rgba_blit(&pb, width / 2, height / 2, &fpb);

	// Now we have a simple image, so write it to a file
	int err = write_PPM("test_blit.ppm", &pb);


int main(int argc, char **argv)

	return 0;

Setup a pixel buffer that is 640 x 480. Draw a rectangle into the pixel buffer (blue color). Copy that frame into another location in the same pixel buffer. Write the pixel buffer out to a file.


And that’s about it.

Some basic constants, simple data structures, core assumptions, and pixels are being stuffed into a buffered in such a way that you can view a picture on your screen.

Next up, drawing lines and rectangles, and what is a ppm file anyway?

GraphicC – What’s so special about graphics anyway?

I have done graphics libraries off and on over the past few decades of programming.  I wanted to take one more crack at it, just because it’s a fun pasttime.  My efforts are on github in the graphicc repository.  This time around, I had some loose design criteria to work from.

  • Use the simplest C constructs as possible
  • Make it small enough to work on a microcontroller
  • Make it flexible enough to be included in any project
  • Make it composable, so that different design tradeoffs can be made
  • Do 2D basics
  • Do 3D basics

These aren’t exactly hard core criteria, but they’re good enough of a constraint for me to get started.  What followed was a lot of fumbling about, writing, rewriting, trying out, testing, and rewriting.  It continues to evolve, and shrink in size.  What of the key aspects of the project is trying to discover the elegant design.  This is something that I have tried to do over the years, no matter what piece of engineering I’m working on, whether it be a machine, workbench, software system, or what have you.  It’s relatively easy to come up with brute force designs that get the job done.  It’s relatively hard to come up with the design that gets the job done with at minimal expense.

When doing a graphics system, it’s really easy to lose focus and get locked into things that you might find on the host platform.  For example, Simple Direct Media Layer (SDL) is available everywhere, so why would anyone build a window and basic graphics interface today?  Well, SDL is more than I’m shooting for.  Over time, my design constraints may line up with those of SDL, and at such time I’ll have a decision to make about switching to using it.  But, to begin, it’s more than I need.

There are tons of other libraries that might suit the bill as well:

There are literally hundreds to choose from.  Some are commercial, some very mature, some old and abandoned.  Some rely on platform specifics, whether it be X or OpenGL, or DirectX.  Some are completely independent, but are tightly integrated with frameworks.  Some are just right, and exactly what I would use, but have some very stiff license terms that are unpleasant.  This is not to say that a perfect solution does not exist, but there’s enough leeway for me to justify to myself that I can spend time on writing this code.

How to start?  Well, first, I consider my various criteria.  The 3D aspects can easily dominate the entirety of the library.  I’m not after creating a gaming library, but I have similar criteria.  I want to be able to simply display 3D models, whether they be renderings of .stl files, or simple ray traces.  I’m not after creating a library that will support the next Destiny on its own, but creating such a library should be possible standing on the shoulders of graphicc.  That means taking care of some basic linear algebra at the very least, and considering various structures.

In the beginning, there was graphicc.h

Here’s a snippet:

#pragma once 

#ifndef graphicc_h
#define graphicc_h

#include &lt;stdint.h&gt;

typedef double REAL;

// Some useful constants
#ifndef M_PI
#define M_PI			3.14159265358979323846264338327950288
#define M_ROOT_PI		1.772453850905516027
#define M_HALF_PI		1.57079632679489661923132169163975144
#define M_QUARTER_PI	0.785398163397448309615660845819875721
#define M_ONE_OVER_PI	0.318309886183790671537767526745028724

#define M_E				2.71828182845904523536
#define M_EULER			0.577215664901532860606

#define M_GOLDEN_RATIO	1.61803398874989484820458683436563811


#define DEGREES(radians) ((180 / M_PI) * radians)
#define RADIANS(degrees) ((M_PI/180)*degrees)

From the very first lines, I am making some design decisions about the language environments in which this code will operate. The ‘pragma once’ is fairly typical of modern C++ compilers. It takes care of only including a header file once in a mass compilation. But, since not all compilers deal with that, there’s the more classic ‘ifndef’ as well.

I do make other assumptions.  including stdint.h.  I’m going to assume this file exists, and contains things like uint8_t.  I’m going to assume that whomever is compiling this code can make sure stdint.h is available, or substitutes appropriate typedefs to make it so.

Then there’s those monsterous constants done as #define statements.  I could do them as const double XXX, but who knows if that’s right for the platform or not.  Again, it’s easily changeable by whomever is compiling the unit.

Then there’s the ‘typedef double REAL’.  I use ‘REAL’ throughout the library because I don’t want to assume ‘double’ is the preferred type on any given platform.  This makes it relatively easy to change to ‘typedef float REAL’ if you so choose.  Of course each one has a different level of precision, and range, so that needs to be accounted for.  The assumption here is that whomever is doing the compilation will know what they want, and if they don’t sticking with a double is a good default.

The various constants are there mainly because they come up time and again when doing simple math for graphics, so they might as well be readily available.  Same goes for the two conversion routines between degrees and radians.  Of course I should change the divisions to be constants for increased speed.

The rest of this header contains some basic types:

typedef REAL real2[2];
typedef REAL real3[3];
typedef REAL real4[4];

typedef struct _mat2 {
REAL m11, m12;
REAL m21, m22;
} mat2;

typedef struct _mat3 {
REAL m11, m12, m13;
REAL m21, m22, m23;
REAL m31, m32, m33;
} mat3;

typedef struct _mat4 {
REAL m11, m12, m13, m14;
REAL m21, m22, m23, m24;
REAL m31, m32, m33, m34;
REAL m41, m42, m43, m44;
} mat4;

enum pixellayouts {

All of these, except the ‘pixellayouts’ are related primarily to 3D graphics.  They are widely used though, so they find themselves in this central header.  Later, there are decisions about doing things like Catmull-Rom splines using matrices.  These are best done using 4×4 matrices, even if you’re just calculating for 2D curves.

Before I go any further, a picture is worth a thousand words no?


This is demonstrating a few things.  Here’s the code:

#include &quot;test_common.h&quot;

void checkerboard(pb_rgba *pb, const size_t cols, const size_t rows, const size_t width, const size_t height, int color1, int color2)
size_t tilewidth = width / cols;
size_t tileheight = (height / rows);

for (size_t c = 0; c &lt; cols; c++){
for (size_t r = 0; r &lt; rows; r++){
raster_rgba_rect_fill(pb, c*tilewidth, r*tileheight, tilewidth / 2, tileheight / 2, color1);
raster_rgba_rect_fill(pb, (c*tilewidth) + tilewidth / 2, r*tileheight, tilewidth / 2, tileheight / 2, color2);
raster_rgba_rect_fill(pb, c*tilewidth, (r*tileheight) + tileheight / 2, tilewidth / 2, tileheight / 2, color2);
raster_rgba_rect_fill(pb, (c*tilewidth) + tilewidth / 2, (r*tileheight) + tileheight / 2, tilewidth / 2, tileheight / 2, color1);

void test_blender()
size_t width = 800;
size_t height = 600;

pb_rgba pb;
pb_rgba_init(&amp;pb, width, height);

// Red background
raster_rgba_rect_fill(&amp;pb, 0, 0, width, height, pRed);

// create checkerboard background
checkerboard(&amp;pb, 16, 16, width, height, pLightGray, pYellow);

// Draw some blended rectangles atop the whole
for (int offset = 10; offset &lt; 400; offset += 40) {
float factor = offset / 400.0f;
int alpha = (int)(factor * 255);
//printf(&quot;factor: %f alpha: %d\n&quot;, factor, alpha);

int fgColor = RGBA(0, 255, 255, alpha);
raster_rgba_rect_fill_blend(&amp;pb, offset, offset, 100, 100, fgColor);

// Now we have a simple image, so write it to a file
int err = write_PPM(&quot;test_blender.ppm&quot;, &amp;pb);

int main(int argc, char **argv)

return 0;

Initializing a pixel buffer (a rendering surface), filling it with a checkerboard pattern, then blending progressively opaque rectangles atop that.  Finally, it writes the result out to a ‘.ppm’ file.  There’s a long way from some constant definitions to doing blended rectangle rendering, but each step is pretty simple, and builds upon the previous.  So, that’s what I’ll focus on next.  In the meanwhile, there’s always to code.