488 lines
9.7 KiB
TypeScript
488 lines
9.7 KiB
TypeScript
/**
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* Clamp a value into a range.
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* @param n
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* @param min
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*/
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export function clamp(n: number, min: number): number
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export function clamp(n: number, min: number, max: number): number
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export function clamp(n: number, min: number, max?: number): number {
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return Math.max(min, typeof max !== 'undefined' ? Math.min(n, max) : n)
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}
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/**
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* Negate a vector.
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* @param A
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*/
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export function neg(A: number[]) {
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return [-A[0], -A[1]]
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}
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/**
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* Add vectors.
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* @param A
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* @param B
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*/
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export function add(A: number[], B: number[]) {
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return [A[0] + B[0], A[1] + B[1]]
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}
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/**
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* Add scalar to vector.
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* @param A
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* @param B
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*/
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export function addScalar(A: number[], n: number) {
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return [A[0] + n, A[1] + n]
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}
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/**
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* Subtract vectors.
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* @param A
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* @param B
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*/
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export function sub(A: number[], B: number[]) {
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return [A[0] - B[0], A[1] - B[1]]
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}
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/**
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* Subtract scalar from vector.
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* @param A
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* @param B
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*/
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export function subScalar(A: number[], n: number) {
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return [A[0] - n, A[1] - n]
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}
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/**
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* Get the vector from vectors A to B.
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* @param A
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* @param B
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*/
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export function vec(A: number[], B: number[]) {
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// A, B as vectors get the vector from A to B
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return [B[0] - A[0], B[1] - A[1]]
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}
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/**
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* Vector multiplication by scalar
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* @param A
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* @param n
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*/
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export function mul(A: number[], n: number) {
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return [A[0] * n, A[1] * n]
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}
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export function mulV(A: number[], B: number[]) {
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return [A[0] * B[0], A[1] * B[1]]
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}
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/**
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* Vector division by scalar.
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* @param A
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* @param n
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*/
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export function div(A: number[], n: number) {
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return [A[0] / n, A[1] / n]
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}
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/**
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* Vector division by vector.
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* @param A
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* @param n
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*/
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export function divV(A: number[], B: number[]) {
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return [A[0] / B[0], A[1] / B[1]]
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}
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/**
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* Perpendicular rotation of a vector A
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* @param A
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*/
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export function per(A: number[]) {
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return [A[1], -A[0]]
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}
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/**
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* Dot product
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* @param A
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* @param B
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*/
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export function dpr(A: number[], B: number[]) {
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return A[0] * B[0] + A[1] * B[1]
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}
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/**
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* Cross product (outer product) | A X B |
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* @param A
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* @param B
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*/
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export function cpr(A: number[], B: number[]) {
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return A[0] * B[1] - B[0] * A[1]
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}
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/**
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* Length of the vector squared
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* @param A
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*/
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export function len2(A: number[]) {
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return A[0] * A[0] + A[1] * A[1]
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}
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/**
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* Length of the vector
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* @param A
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*/
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export function len(A: number[]) {
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return Math.hypot(A[0], A[1])
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}
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/**
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* Project A over B
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* @param A
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* @param B
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*/
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export function pry(A: number[], B: number[]) {
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return dpr(A, B) / len(B)
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}
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/**
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* Get normalized / unit vector.
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* @param A
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*/
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export function uni(A: number[]) {
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return div(A, len(A))
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}
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/**
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* Get normalized / unit vector.
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* @param A
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*/
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export function normalize(A: number[]) {
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return uni(A)
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}
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/**
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* Get the tangent between two vectors.
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* @param A
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* @param B
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* @returns
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*/
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export function tangent(A: number[], B: number[]) {
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return normalize(sub(A, B))
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}
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/**
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* Dist length from A to B squared.
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* @param A
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* @param B
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*/
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export function dist2(A: number[], B: number[]) {
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return len2(sub(A, B))
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}
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/**
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* Dist length from A to B
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* @param A
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* @param B
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*/
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export function dist(A: number[], B: number[]) {
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return Math.hypot(A[1] - B[1], A[0] - B[0])
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}
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/**
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* A faster, though less accurate method for testing distances. Maybe faster?
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* @param A
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* @param B
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* @returns
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*/
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export function fastDist(A: number[], B: number[]) {
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const V = [B[0] - A[0], B[1] - A[1]]
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const aV = [Math.abs(V[0]), Math.abs(V[1])]
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let r = 1 / Math.max(aV[0], aV[1])
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r = r * (1.29289 - (aV[0] + aV[1]) * r * 0.29289)
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return [V[0] * r, V[1] * r]
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}
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/**
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* Angle between vector A and vector B in radians
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* @param A
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* @param B
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*/
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export function ang(A: number[], B: number[]) {
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return Math.atan2(cpr(A, B), dpr(A, B))
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}
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/**
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* Angle between vector A and vector B in radians
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* @param A
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* @param B
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*/
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export function angle(A: number[], B: number[]) {
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return Math.atan2(B[1] - A[1], B[0] - A[0])
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}
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/**
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* Mean between two vectors or mid vector between two vectors
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* @param A
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* @param B
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*/
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export function med(A: number[], B: number[]) {
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return mul(add(A, B), 0.5)
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}
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/**
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* Vector rotation by r (radians)
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* @param A
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* @param r rotation in radians
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*/
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export function rot(A: number[], r: number) {
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return [
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A[0] * Math.cos(r) - A[1] * Math.sin(r),
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A[0] * Math.sin(r) + A[1] * Math.cos(r),
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]
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}
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/**
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* Rotate a vector around another vector by r (radians)
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* @param A vector
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* @param C center
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* @param r rotation in radians
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*/
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export function rotWith(A: number[], C: number[], r: number) {
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if (r === 0) return A
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const s = Math.sin(r)
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const c = Math.cos(r)
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const px = A[0] - C[0]
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const py = A[1] - C[1]
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const nx = px * c - py * s
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const ny = px * s + py * c
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return [nx + C[0], ny + C[1]]
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}
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/**
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* Check of two vectors are identical.
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* @param A
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* @param B
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*/
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export function isEqual(A: number[], B: number[]) {
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return A[0] === B[0] && A[1] === B[1]
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}
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/**
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* Interpolate vector A to B with a scalar t
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* @param A
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* @param B
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* @param t scalar
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*/
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export function lrp(A: number[], B: number[], t: number) {
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return add(A, mul(vec(A, B), t))
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}
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/**
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* Interpolate from A to B when curVAL goes fromVAL => to
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* @param A
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* @param B
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* @param from Starting value
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* @param to Ending value
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* @param s Strength
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*/
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export function int(A: number[], B: number[], from: number, to: number, s = 1) {
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const t = (clamp(from, to) - from) / (to - from)
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return add(mul(A, 1 - t), mul(B, s))
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}
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/**
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* Get the angle between the three vectors A, B, and C.
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* @param p1
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* @param pc
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* @param p2
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*/
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export function ang3(p1: number[], pc: number[], p2: number[]) {
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// this,
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const v1 = vec(pc, p1)
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const v2 = vec(pc, p2)
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return ang(v1, v2)
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}
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/**
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* Absolute value of a vector.
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* @param A
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* @returns
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*/
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export function abs(A: number[]) {
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return [Math.abs(A[0]), Math.abs(A[1])]
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}
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export function rescale(a: number[], n: number) {
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const l = len(a)
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return [(n * a[0]) / l, (n * a[1]) / l]
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}
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/**
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* Get whether p1 is left of p2, relative to pc.
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* @param p1
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* @param pc
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* @param p2
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*/
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export function isLeft(p1: number[], pc: number[], p2: number[]) {
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// isLeft: >0 for counterclockwise
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// =0 for none (degenerate)
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// <0 for clockwise
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return (pc[0] - p1[0]) * (p2[1] - p1[1]) - (p2[0] - p1[0]) * (pc[1] - p1[1])
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}
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export function clockwise(p1: number[], pc: number[], p2: number[]) {
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return isLeft(p1, pc, p2) > 0
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}
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const rounds = [1, 10, 100, 1000]
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export function round(a: number[], d = 2) {
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return [
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Math.round(a[0] * rounds[d]) / rounds[d],
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Math.round(a[1] * rounds[d]) / rounds[d],
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]
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}
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/**
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* Get the minimum distance from a point P to a line with a segment AB.
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* @param A The start of the line.
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* @param B The end of the line.
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* @param P A point.
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* @returns
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*/
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// export function distanceToLine(A: number[], B: number[], P: number[]) {
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// const delta = sub(B, A)
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// const angle = Math.atan2(delta[1], delta[0])
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// const dir = rot(sub(P, A), -angle)
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// return dir[1]
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// }
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/**
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* Get the nearest point on a line segment AB.
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* @param A The start of the line.
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* @param B The end of the line.
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* @param P A point.
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* @param clamp Whether to clamp the resulting point to the segment.
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* @returns
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*/
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// export function nearestPointOnLine(
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// A: number[],
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// B: number[],
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// P: number[],
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// clamp = true
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// ) {
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// const delta = sub(B, A)
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// const length = len(delta)
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// const angle = Math.atan2(delta[1], delta[0])
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// const dir = rot(sub(P, A), -angle)
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// if (clamp) {
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// if (dir[0] < 0) return A
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// if (dir[0] > length) return B
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// }
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// return add(A, div(mul(delta, dir[0]), length))
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// }
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/**
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* Get the nearest point on a line with a known unit vector that passes through point A
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* @param A Any point on the line
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* @param u The unit vector for the line.
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* @param P A point not on the line to test.
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* @returns
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*/
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export function nearestPointOnLineThroughPoint(
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A: number[],
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u: number[],
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P: number[]
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) {
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return add(A, mul(u, pry(sub(P, A), u)))
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}
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/**
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* Distance between a point and a line with a known unit vector that passes through a point.
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* @param A Any point on the line
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* @param u The unit vector for the line.
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* @param P A point not on the line to test.
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* @returns
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*/
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export function distanceToLineThroughPoint(
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A: number[],
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u: number[],
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P: number[]
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) {
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return dist(P, nearestPointOnLineThroughPoint(A, u, P))
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}
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/**
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* Get the nearest point on a line segment between A and B
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* @param A The start of the line segment
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* @param B The end of the line segment
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* @param P The off-line point
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* @param clamp Whether to clamp the point between A and B.
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* @returns
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*/
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export function nearestPointOnLineSegment(
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A: number[],
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B: number[],
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P: number[],
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clamp = true
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) {
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const delta = sub(B, A)
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const length = len(delta)
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const u = div(delta, length)
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const pt = add(A, mul(u, pry(sub(P, A), u)))
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if (clamp) {
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const da = dist(A, pt)
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const db = dist(B, pt)
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if (db < da && da > length) return B
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if (da < db && db > length) return A
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}
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return pt
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}
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/**
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* Distance between a point and the nearest point on a line segment between A and B
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* @param A The start of the line segment
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* @param B The end of the line segment
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* @param P The off-line point
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* @param clamp Whether to clamp the point between A and B.
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* @returns
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*/
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export function distanceToLineSegment(
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A: number[],
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B: number[],
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P: number[],
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clamp = true
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) {
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return dist(P, nearestPointOnLineSegment(A, B, P, clamp))
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}
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/**
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* Get a vector d distance from A towards B.
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* @param A
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* @param B
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* @param d
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* @returns
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*/
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export function nudge(A: number[], B: number[], d: number) {
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return add(A, mul(uni(vec(A, B)), d))
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}
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/**
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* Round a vector to a precision length.
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* @param a
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* @param n
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*/
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export function toPrecision(a: number[], n = 4) {
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return [+a[0].toPrecision(n), +a[1].toPrecision(n)]
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}
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