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| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 | 4x 4x 5x 1x 1x 1x 1x 1x 1x 1x 1x 36x 9x 9x 15x 15x 15x 3x 3x 3x 3x 3x 3x 3x 3x | import { Point3, Plane } from '../types';
import { vec3, mat3 } from 'gl-matrix';
/**
* It calculates the intersection of a line and a plane.
* Plane equation is Ax+By+Cz=D
* @param p0 - [x,y,z] of the first point of the line
* @param p1 - [x,y,z] of the second point of the line
* @param plane - [A, B, C, D] Plane parameter: Ax+By+Cz=D
* @returns - [X,Y,Z] coordinates of the intersection
*/
function linePlaneIntersection(p0: Point3, p1: Point3, plane: Plane): Point3 {
const [x0, y0, z0] = p0;
const [x1, y1, z1] = p1;
const [A, B, C, D] = plane;
const a = x1 - x0;
const b = y1 - y0;
const c = z1 - z0;
const t = (-1 * (A * x0 + B * y0 + C * z0 - D)) / (A * a + B * b + C * c);
const X = a * t + x0;
const Y = b * t + y0;
const Z = c * t + z0;
return [X, Y, Z];
}
/**
* It returns the plane equation defined by a point and a normal vector.
* @param normal - normal vector
* @param point - a point on the plane
* @returns - [A, B,C, D] of plane equation A*X + B*Y + C*Z = D
*/
function planeEquation(normal: Point3, point: Point3 | vec3): Plane {
const [A, B, C] = normal;
const D = A * point[0] + B * point[1] + C * point[2];
return [A, B, C, D];
}
/**
* Computes the intersection of three planes in 3D space with equations:
* A1*X + B1*Y + C1*Z = D1
* A2*X + B2*Y + C2*Z = D2
* A3*X + B3*Y + C3*Z = D3
* @returns - [x, y, z] the intersection in the world coordinate
*/
function threePlaneIntersection(
firstPlane: Plane,
secondPlane: Plane,
thirdPlane: Plane
): Point3 {
const [A1, B1, C1, D1] = firstPlane;
const [A2, B2, C2, D2] = secondPlane;
const [A3, B3, C3, D3] = thirdPlane;
const m0 = mat3.fromValues(A1, A2, A3, B1, B2, B3, C1, C2, C3);
const m1 = mat3.fromValues(D1, D2, D3, B1, B2, B3, C1, C2, C3);
const m2 = mat3.fromValues(A1, A2, A3, D1, D2, D3, C1, C2, C3);
const m3 = mat3.fromValues(A1, A2, A3, B1, B2, B3, D1, D2, D3);
// TODO: handle no intersection scenario
const x = mat3.determinant(m1) / mat3.determinant(m0);
const y = mat3.determinant(m2) / mat3.determinant(m0);
const z = mat3.determinant(m3) / mat3.determinant(m0);
return [x, y, z];
}
/**
* Computes the distance of a point in 3D space to a plane
* @param plane - [A, B, C, D] of plane equation A*X + B*Y + C*Z = D
* @param point - [A, B, C] the plane in World coordinate
* @param signed - if true, the distance is signed
* @returns - the distance of the point to the plane
* */
function planeDistanceToPoint(
plane: Plane,
point: Point3,
signed = false
): number {
const [A, B, C, D] = plane;
const [x, y, z] = point;
const numerator = A * x + B * y + C * z - D;
const distance = Math.abs(numerator) / Math.sqrt(A * A + B * B + C * C);
const sign = signed ? Math.sign(numerator) : 1;
return sign * distance;
}
export {
linePlaneIntersection,
planeEquation,
threePlaneIntersection,
planeDistanceToPoint,
};
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