gpu/internal/shaders: generate shader variants

We're about to add Direct3D support, where shaders are written in
HLSL. Rather than write shaders twice (or more), convert them to
a GLSL variant understood by the glslcc cross-compiler and generate
the OpenGL ES 2.0 and HLSL variants. The HLSL is used by a future
change.

Signed-off-by: Elias Naur <mail@eliasnaur.com>

gpu/shaders/stencil.frag

@@ -0,0 +1,83 @@
+#version 310 es
+
+// SPDX-License-Identifier: Unlicense OR MIT
+
+precision mediump float;
+
+layout(location=0) in vec2 vFrom;
+layout(location=1) in vec2 vCtrl;
+layout(location=2) in vec2 vTo;
+
+layout(binding=0) uniform sampler2D areaLUT;
+
+layout(location = 0) out vec4 fragCover;
+
+void main() {
+	float dx = vTo.x - vFrom.x;
+	// Sort from and to in increasing order so the root below
+	// is always the positive square root, if any.
+	// We need the direction of the curve below, so this can't be
+	// done from the vertex shader.
+	bool increasing = vTo.x >= vFrom.x;
+	vec2 left = increasing ? vFrom : vTo;
+	vec2 right = increasing ? vTo : vFrom;
+
+	// The signed horizontal extent of the fragment.
+	vec2 extent = clamp(vec2(vFrom.x, vTo.x), -0.5, 0.5);
+	// Find the t where the curve crosses the middle of the
+	// extent, x₀.
+	// Given the Bézier curve with x coordinates P₀, P₁, P₂
+	// where P₀ is at the origin, its x coordinate in t
+	// is given by:
+	//
+	// x(t) = 2(1-t)tP₁ + t²P₂
+	// 
+	// Rearranging:
+	//
+	// x(t) = (P₂ - 2P₁)t² + 2P₁t
+	//
+	// Setting x(t) = x₀ and using Muller's quadratic formula ("Citardauq")
+	// for robustnesss,
+	//
+	// t = 2x₀/(2P₁±√(4P₁²+4(P₂-2P₁)x₀))
+	//
+	// which simplifies to
+	//
+	// t = x₀/(P₁±√(P₁²+(P₂-2P₁)x₀))
+	//
+	// Setting v = P₂-P₁,
+	//
+	// t = x₀/(P₁±√(P₁²+(v-P₁)x₀))
+	//
+	// t lie in [0; 1]; P₂ ≥ P₁ and P₁ ≥ 0 since we split curves where
+	// the control point lies before the start point or after the end point.
+	// It can then be shown that only the positive square root is valid.
+	float midx = mix(extent.x, extent.y, 0.5);
+	float x0 = midx - left.x;
+	vec2 p1 = vCtrl - left;
+	vec2 v = right - vCtrl;
+	float t = x0/(p1.x+sqrt(p1.x*p1.x+(v.x-p1.x)*x0));
+	// Find y(t) on the curve.
+	float y = mix(mix(left.y, vCtrl.y, t), mix(vCtrl.y, right.y, t), t);
+	// And the slope.
+	vec2 d_half = mix(p1, v, t);
+	float dy = d_half.y/d_half.x;
+	// Together, y and dy form a line approximation.
+
+	// Compute the fragment area above the line.
+	// The area is symmetric around dy = 0. Scale slope with extent width.
+	float width = extent.y - extent.x;
+	dy = abs(dy*width);
+
+	vec4 sides = vec4(dy*+0.5 + y, dy*-0.5 + y, (+0.5-y)/dy, (-0.5-y)/dy);
+	sides = clamp(sides+0.5, 0.0, 1.0);
+
+	float area = 0.5*(sides.z - sides.z*sides.y + 1.0 - sides.x+sides.x*sides.w);
+	area *= width;
+
+	// Work around issue #13.
+	if (width == 0.0)
+		area = 0.0;
+
+	fragCover.r = area;
+}