Luxe polar warp shader

polarWarp.glsl

//The source texture that will be transformed
uniform sampler2D tex0;

//The texture coordinate passed in from the vertex shader (the default luxe vertex shader is suffice)
varying vec2 tcoord;

//x: width of the texture divided by the radius that represents the top of the image (normally screen width / radius)
//y: height of the texture divided by the radius representing the top of the image (normally screen height / radius)
uniform vec2 sizeOverRadius;

//This is a constant to determine how far left/right on the source image we look for additional samples 
//to counteract thin lines disappearing towards the center (a somewhat adjusted texel width in uv-coordinates)
//This value is 1 / (texture width * 2 PI)
uniform float sampleOffset;

//Linear blend factor that swaps the direction the y-axis of the source is mapped onto the radius
//if the value is 1, y = 0 is at the outer edge of the circle, 
//if the value is 0, y = 0 is the center of the circle
uniform float polarFactor;

void main() {
	
	//Make relative to center
	vec2 relPos = tcoord - vec2(0.5,0.5);
	
	//Adjust for screen ratio
	relPos *= sizeOverRadius;
	
	//Normalised polar coordinates.
	//y: radius from center
	//x: angle
	vec2 polar;
	
	polar.y = sqrt(relPos.x * relPos.x + relPos.y * relPos.y);
	
	//Any radius over 1 would go beyond the source texture size, this simply outputs black for those fragments
	if(polar.y > 1.0){
		gl_FragColor = vec4(0.0, 0.0, 0.0, 1.0);
		return;
	}
	
	polar.x = atan(relPos.y, relPos.x);
	
	//Normally, the angle starts from the axis going right and is counter-clockwise
	//I want the left edge of the screen image to be the line upwards,
	//so I rotate the angle half pi clockwise
	polar.x -= 1.57079632679;
	
	//Normalise from angle to 0-1 range
	polar.x /= 6.28318530718;
	
	//Make clockwise
	polar.x = -polar.x;
	
	polar.x = mod(polar.x, 1.0);
	
	//The xOffset fixes lines disappearing towards the center of the coordinate system
	//This happens because there's only a few pixels trying to display the whole width of the source image
	//so they 'miss' the lines. To fix this, we sample at the transformed position
	//and a bit to the left and right of it to catch anything we might miss.
	//Using 1 / radius gives us minimal offset far out from the circle, 
	//and a wide offset for pixels close to the center
	
	float xOffset = 0.0;
	if(polar.y != 0.0){
		xOffset = 1.0 / polar.y;
	}
	
	//Adjusts for texture resolution
	xOffset *= sampleOffset;
	
	//This inverts the radius variable depending on the polarFactor
	polar.y = polar.y * polarFactor + (1.0 - polar.y) * (1.0 - polarFactor);
	
	//Sample at positions with a slight offset
	vec4 one = texture2D(tex0, vec2(polar.x - xOffset, polar.y));
	
	vec4 two = texture2D(tex0, polar);
	
	vec4 three = texture2D(tex0, vec2(polar.x + xOffset, polar.y));
	
	//Take the maximum of the three samples. This is not ideal, but the quickest way to choose a coloured sample over the background colour.
	gl_FragColor = max(max(one, two), three);
}