Fisheye Skybox Shader - glsl

Question

I'm trying to write a panaorama viewer. Mostly this involves mapping an image to a quad to simulate a skybox.
For a cubemap image it's pretty trival. Either copy the 6 parts of the image to a 6 planes of a cube map or else make a shader that does the cubemap math as specified in the OpenGL ES spec
For an equirectangular image like from a Ricoh Theta
you can use this math
// convert from direction (n) to texcoord (uv)
float latitude = acos(n.y);
float longitude = atan(n.z, n.x);
vec2 sphereCoords = vec2(longitude, latitude) * vec2(0.5 / PI, 1.0 / PI);
vec2 uv = fract(vec2(0.5,1.0) - sphereCoords);
const m4 = twgl.m4;
const gl = document.querySelector('canvas').getContext('webgl');
const vs = `
attribute vec4 position;
varying vec4 v_position;
void main() {
v_position = position;
gl_Position = position;
gl_Position.z = 1.0;
}
`;
const fs = `
precision highp float;
uniform sampler2D u_skybox;
uniform mat4 u_viewDirectionProjectionInverse;
varying vec4 v_position;
#define PI radians(180.0)
void main() {
vec4 t = u_viewDirectionProjectionInverse * v_position;
vec3 n = normalize(t.xyz / t.w);
// convert from direction (n) to texcoord (uv)
float latitude = acos(n.y);
float longitude = atan(n.z, n.x);
vec2 sphereCoords = vec2(longitude, latitude) * vec2(0.5 / PI, 1.0 / PI);
vec2 uv = fract(vec2(0.5,1.0) - sphereCoords);
// multiply u by 2 because we only have a 180degree view
gl_FragColor = texture2D(u_skybox, uv * vec2(-2, 1));
}
`;
const programInfo = twgl.createProgramInfo(gl, [vs, fs]);
const tex = twgl.createTexture(gl, {
src: 'https://i.imgur.com/ChIfXM0.jpg',
flipY: true,
});
const bufferInfo = twgl.primitives.createXYQuadBufferInfo(gl, 2);
function render(time) {
time *= 0.001;
twgl.resizeCanvasToDisplaySize(gl.canvas);
gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);
const aspect = gl.canvas.clientWidth / gl.canvas.clientHeight;
const projectionMatrix = m4.perspective(45 * Math.PI / 180, aspect, 1, 20);
const cameraMatrix = m4.rotationY(time * 0.1);
m4.rotateX(cameraMatrix, Math.sin(time * 0.3) * 0.5, cameraMatrix);
const viewMatrix = m4.inverse(cameraMatrix);
viewMatrix[12] = 0;
viewMatrix[13] = 0;
viewMatrix[14] = 0;
const viewDirectionProjectionMatrix = m4.multiply(projectionMatrix, viewMatrix);
const viewDirectionProjectionInverseMatrix = m4.inverse(viewDirectionProjectionMatrix);
gl.useProgram(programInfo.program);
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
twgl.setUniforms(programInfo, {
u_viewDirectionProjectionInverse: viewDirectionProjectionInverseMatrix,
u_skyBox: tex,
});
twgl.drawBufferInfo(gl, bufferInfo);
requestAnimationFrame(render);
}
requestAnimationFrame(render);
body { margin: 0; }
canvas { width: 100vw; height: 100vh; display: block; }
<script src="https://twgljs.org/dist/4.x/twgl-full.min.js"></script>
<canvas></canvas>
But some images are not equirectangular, they're fisheye?
I've been trying to figure out the math needed to do the same thing (map this to a quad based skybox) but I've been having no luck
As a reference I found this page with conversions from 3d to fisheye coords. It says
// convert from direction (n) to texcoord (uv)
float r = 2.0 * atan(length(n.xy), n.z) / PI;
float theta = atan(n.y, n.x);
vec2 uv = vec2(cos(theta), sin(theta)) * r * 0.5 + 0.5;
const m4 = twgl.m4;
const gl = document.querySelector('canvas').getContext('webgl');
const vs = `
attribute vec4 position;
varying vec4 v_position;
void main() {
v_position = position;
gl_Position = position;
gl_Position.z = 1.0;
}
`;
const fs = `
precision highp float;
uniform sampler2D u_skybox;
uniform mat4 u_viewDirectionProjectionInverse;
varying vec4 v_position;
#define PI radians(180.0)
void main() {
vec4 t = u_viewDirectionProjectionInverse * v_position;
vec3 n = normalize(t.xyz / t.w);
// convert from direction (n) to texcoord (uv)
float r = 2.0 * atan(length(n.xy), n.z) / PI;
float theta = atan(n.y, n.x);
vec2 uv = vec2(cos(theta), sin(theta)) * r * 0.5 + 0.5;
#if 0
// Calculate fisheye angle and radius
float theta = atan(n.z, n.x);
float phi = atan(length(n.xz), n.y);
float r = phi / PI;
// Pixel in fisheye space
vec2 uv = vec2(0.5) + r * vec2(cos(theta), sin(theta));
#endif
// multiply u by 2 because we only have a 180degree view
gl_FragColor = texture2D(u_skybox, uv * vec2(-2, 1));
}
`;
const programInfo = twgl.createProgramInfo(gl, [vs, fs]);
const tex = twgl.createTexture(gl, {
src: 'https://i.imgur.com/dzXCQwM.jpg',
flipY: true,
});
const bufferInfo = twgl.primitives.createXYQuadBufferInfo(gl, 2);
function render(time) {
time *= 0.001;
twgl.resizeCanvasToDisplaySize(gl.canvas);
gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);
const aspect = gl.canvas.clientWidth / gl.canvas.clientHeight;
const projectionMatrix = m4.perspective(45 * Math.PI / 180, aspect, 1, 20);
const cameraMatrix = m4.rotationY(time * 0.1);
m4.rotateX(cameraMatrix, 0.7 + Math.sin(time * 0.3) * .7, cameraMatrix);
const viewMatrix = m4.inverse(cameraMatrix);
viewMatrix[12] = 0;
viewMatrix[13] = 0;
viewMatrix[14] = 0;
const viewDirectionProjectionMatrix = m4.multiply(projectionMatrix, viewMatrix);
const viewDirectionProjectionInverseMatrix = m4.inverse(viewDirectionProjectionMatrix);
gl.useProgram(programInfo.program);
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
twgl.setUniforms(programInfo, {
u_viewDirectionProjectionInverse: viewDirectionProjectionInverseMatrix,
u_skyBox: tex,
});
twgl.drawBufferInfo(gl, bufferInfo);
requestAnimationFrame(render);
}
requestAnimationFrame(render);
body { margin: 0; }
canvas { width: 100vw; height: 100vh; display: block; }
<script src="https://twgljs.org/dist/4.x/twgl-full.min.js"></script>
<canvas></canvas>
Also this
Clearly I'm missing something.

Answer 1

I believe the error lies in this logic:
// multiply u by 2 because we only have a 180degree view
gl_FragColor = texture2D(u_skybox, uv * vec2(-2, 1));
Although this works in the equirectangular case because the math works out such that the z-component only affects longitude, it is no longer valid in the fisheye case because n.z affects both axes.
You can account for the negative z-component in the formula by taking the absolute value of n.z and flipping n.x when the z is negative:
// convert from direction (n) to texcoord (uv)
float r = 2.0 * atan(length(n.xy), abs(n.z)) / PI;
float theta = atan(n.y, n.x * sign(n.z));
vec2 uv = vec2(cos(theta), sin(theta)) * r * 0.5 + vec2(0.5);
Here it is in action:
const m4 = twgl.m4;
const gl = document.querySelector('canvas').getContext('webgl');
const vs = `
attribute vec4 position;
varying vec4 v_position;
void main() {
v_position = position;
gl_Position = position;
gl_Position.z = 1.0;
}
`;
const fs = `
precision highp float;
uniform sampler2D u_skybox;
uniform mat4 u_viewDirectionProjectionInverse;
varying vec4 v_position;
#define PI radians(180.0)
void main() {
vec4 t = u_viewDirectionProjectionInverse * v_position;
vec3 n = normalize(t.xyz / t.w);
// convert from direction (n) to texcoord (uv)
float r = 2.0 * atan(length(n.xy), abs(n.z)) / PI;
float theta = atan(n.y, n.x * sign(n.z));
vec2 uv = vec2(cos(theta), sin(theta)) * r * 0.5 + vec2(0.5);
gl_FragColor = texture2D(u_skybox, uv * vec2(-1.0, 1.0));
}
`;
const programInfo = twgl.createProgramInfo(gl, [vs, fs]);
const tex = twgl.createTexture(gl, {
src: 'https://i.imgur.com/dzXCQwM.jpg',
flipY: true,
});
const bufferInfo = twgl.primitives.createXYQuadBufferInfo(gl, 2);
function render(time) {
time *= 0.001;
twgl.resizeCanvasToDisplaySize(gl.canvas);
gl.viewport(0, 0, gl.canvas.width, gl.canvas.height);
const aspect = gl.canvas.clientWidth / gl.canvas.clientHeight;
const projectionMatrix = m4.perspective(45 * Math.PI / 180, aspect, 1, 20);
const cameraMatrix = m4.rotationY(time * 0.1);
m4.rotateX(cameraMatrix, 0.7 + Math.sin(time * 0.3) * .7, cameraMatrix);
const viewMatrix = m4.inverse(cameraMatrix);
viewMatrix[12] = 0;
viewMatrix[13] = 0;
viewMatrix[14] = 0;
const viewDirectionProjectionMatrix = m4.multiply(projectionMatrix, viewMatrix);
const viewDirectionProjectionInverseMatrix = m4.inverse(viewDirectionProjectionMatrix);
gl.useProgram(programInfo.program);
twgl.setBuffersAndAttributes(gl, programInfo, bufferInfo);
twgl.setUniforms(programInfo, {
u_viewDirectionProjectionInverse: viewDirectionProjectionInverseMatrix,
u_skyBox: tex,
});
twgl.drawBufferInfo(gl, bufferInfo);
requestAnimationFrame(render);
}
requestAnimationFrame(render);
body { margin: 0; }
canvas { width: 100vw; height: 100vh; display: block; }
<script src="https://twgljs.org/dist/4.x/twgl-full.min.js"></script>
<canvas></canvas>