@woosh/meep-engine/src/core/geom/3d/sphere/sphere_project.js

Pure JavaScript game engine. Fully featured and production ready.

import { assert } from "../../../assert.js";
import { v3_dot } from "../../vec3/v3_dot.js";
import { v4_multiply_mat4 } from "../../vec4/v4_multiply_mat4.js";

const v4 = [];

/**
 * Computations of screen-space pixel area covered by a sphere
 * NOTE: Port of GLSL code by Ingo Quilez. Source: http://www.iquilezles.org/www/articles/sphereproj/sphereproj.htm
 * @param {number[]|{0:number,1:number,2:number,3:number}} sph Sphere in world space
 * @param {number[]|Float32Array} cam camera transform matrix (world to camera)(inverse world matrix of camera)
 * @param {number} fl focal length (fov in Radians)
 * @returns {number} area on the screen as a fraction, 1=entire screen, 0=zero area
 */
export function sphere_project(sph, cam, fl) {
    assert.notNull(cam, 'cam');
    assert.isNumber(fl, 'fl');
    assert.greaterThan(fl, 0, 'fl');

    v4[0] = sph[0];
    v4[1] = sph[1];
    v4[2] = sph[2];
    v4[3] = 1;

    //transform to camera space
    v4_multiply_mat4(v4, v4, cam);

    const r = sph[3];
    const r2 = r * r;

    const v4_x = v4[0];
    const v4_y = v4[1];
    const v4_z = v4[2];

    const z2 = v4_z * v4_z;

    const l2 = v3_dot(v4_x, v4_y, v4_z, v4_x, v4_y, v4_z);

    const rz2 = r2 - z2;

    if (rz2 === 0) {
        // avoid division by 0
        return 0;
    }

    const area = -Math.PI * fl * fl * r2 * Math.sqrt(Math.abs((l2 - r2) / rz2)) / rz2;

    return Math.abs(area);
}