Spline/math.js at master · Jacob-Guglielmin/Spline · GitHub

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
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
"use strict";

function lerp(points, t) {
    let segmentId = Math.floor(t);

    if (segmentId >= points.length - 1) segmentId = points.length - 2;

    let fractional = Math.min(t - segmentId, 1);

    return {
        x: points[segmentId].x + (points[segmentId + 1].x - points[segmentId].x) * fractional,
        y: points[segmentId].y + (points[segmentId + 1].y - points[segmentId].y) * fractional
    };
}

function cubicHermiteCurve(points, t) {
    let velX1 = points[1].x - points[0].x;
    let velY1 = points[1].y - points[0].y;
    let velX2 = points[3].x - points[2].x;
    let velY2 = points[3].y - points[2].y;

    return {
        x: points[0].x + t * velX1 + t ** 2 * (-3 * points[0].x + 3 * points[2].x - 2 * velX1 - velX2) + t ** 3 * (2 * points[0].x - 2 * points[2].x + velX1 + velX2),
        y: points[0].y + t * velY1 + t ** 2 * (-3 * points[0].y + 3 * points[2].y - 2 * velY1 - velY2) + t ** 3 * (2 * points[0].y - 2 * points[2].y + velY1 + velY2)
    };
}

function cubicHermiteCurveDerivative(points, t) {
    let velX1 = points[1].x - points[0].x;
    let velY1 = points[1].y - points[0].y;
    let velX2 = points[3].x - points[2].x;
    let velY2 = points[3].y - points[2].y;

    return {
        x: velX1 + 2 * t * (-3 * points[0].x + 3 * points[2].x - 2 * velX1 - velX2) + 3 * t ** 2 * (2 * points[0].x - 2 * points[2].x + velX1 + velX2),
        y: velY1 + 2 * t * (-3 * points[0].y + 3 * points[2].y - 2 * velY1 - velY2) + 3 * t ** 2 * (2 * points[0].y - 2 * points[2].y + velY1 + velY2)
    };
}

function cubicHermiteSpline(points, t) {
    let segmentId = Math.min(Math.floor(t), points.length / 2 - 2);

    let fractional = Math.min(t - segmentId, 1);

    return cubicHermiteCurve(points.slice(segmentId * 2, segmentId * 2 + 4), fractional);
}

function cubicHermiteSplineDerivative(points, t) {
    let segmentId = Math.min(Math.floor(t), points.length / 2 - 2);

    let fractional = Math.min(t - segmentId, 1);

    return cubicHermiteCurveDerivative(points.slice(segmentId * 2, segmentId * 2 + 4), fractional);
}

function getCardinalSplinePoints(points, scale) {
    let newPoints = [];
    for (let i = 1; i < points.length - 1; i++) {
        //Save point
        newPoints.push(points[i]);

        //Calculate velocity and scale magnitude by scale, then place at appropriate point on curve
        newPoints.push({
            x: (points[i + 1].x - points[i - 1].x) * scale + points[i].x,
            y: (points[i + 1].y - points[i - 1].y) * scale + points[i].y
        });
    }

    return newPoints;
}

function cardinalSpline(points, t, scale) {
    return cubicHermiteSpline(getCardinalSplinePoints(points, scale), t);
}

function arbitraryBezierCurve(points, t) {
    const newPoints = [];

    for (let i = 0; i < points.length - 1; i++) {
        newPoints.push(lerp(points.slice(i, i + 2), t));
    }

    if (newPoints.length === 1) {
        return newPoints[0];
    } else {
        return arbitraryBezierCurve(newPoints, t);
    }
}

function cubicBezierSpline(points, t) {
    let segmentId = Math.min(Math.floor(t), (points.length - 1) / 3 - 1);

    let fractional = Math.min(t - segmentId, 1);

    return {
        x: points[segmentId * 3].x + fractional * (-3 * points[segmentId * 3].x + 3 * points[segmentId * 3 + 1].x) + fractional ** 2 * (3 * points[segmentId * 3].x - 6 * points[segmentId * 3 + 1].x + 3 * points[segmentId * 3 + 2].x) + fractional ** 3 * (-points[segmentId * 3].x + 3 * points[segmentId * 3 + 1].x - 3 * points[segmentId * 3 + 2].x + points[segmentId * 3 + 3].x),
        y: points[segmentId * 3].y + fractional * (-3 * points[segmentId * 3].y + 3 * points[segmentId * 3 + 1].y) + fractional ** 2 * (3 * points[segmentId * 3].y - 6 * points[segmentId * 3 + 1].y + 3 * points[segmentId * 3 + 2].y) + fractional ** 3 * (-points[segmentId * 3].y + 3 * points[segmentId * 3 + 1].y - 3 * points[segmentId * 3 + 2].y + points[segmentId * 3 + 3].y)
    };
}

function cubicBezierSplineDerivative(points, t) {
    let segmentId = Math.min(Math.floor(t), points.length - 2);

    let fractional = Math.min(t - segmentId, 1);

    return {
        x: -3 * points[segmentId * 3].x + 3 * points[segmentId * 3 + 1].x + 2 * fractional * (3 * points[segmentId * 3].x - 6 * points[segmentId * 3 + 1].x + 3 * points[segmentId * 3 + 2].x) + 3 * fractional ** 2 * (-points[segmentId * 3].x + 3 * points[segmentId * 3 + 1].x - 3 * points[segmentId * 3 + 2].x + points[segmentId * 3 + 3].x),
        y: -3 * points[segmentId * 3].y + 3 * points[segmentId * 3 + 1].y + 2 * fractional * (3 * points[segmentId * 3].y - 6 * points[segmentId * 3 + 1].y + 3 * points[segmentId * 3 + 2].y) + 3 * fractional ** 2 * (-points[segmentId * 3].y + 3 * points[segmentId * 3 + 1].y - 3 * points[segmentId * 3 + 2].y + points[segmentId * 3 + 3].y)
    };
}

function oppositeAngledPoint(originalPosition, mirrorAcross, copyAngleFrom) {
    const intendedAngle = Math.atan2(mirrorAcross.y - copyAngleFrom.y, mirrorAcross.x - copyAngleFrom.x);

    const intendedMagnitude = Math.sqrt(Math.pow(mirrorAcross.x - originalPosition.x, 2) + Math.pow(mirrorAcross.y - originalPosition.y, 2));

    const newX = mirrorAcross.x + Math.cos(intendedAngle) * intendedMagnitude;
    const newY = mirrorAcross.y + Math.sin(intendedAngle) * intendedMagnitude;

    return { x: newX, y: newY };
}

function mirroredPoint(mirrorAcross, copyAngleFrom) {
    const intendedAngle = Math.atan2(mirrorAcross.y - copyAngleFrom.y, mirrorAcross.x - copyAngleFrom.x);
    const magnitude = Math.sqrt(Math.pow(mirrorAcross.x - copyAngleFrom.x, 2) + Math.pow(mirrorAcross.y - copyAngleFrom.y, 2));

    const newX = mirrorAcross.x + Math.cos(intendedAngle) * magnitude;
    const newY = mirrorAcross.y + Math.sin(intendedAngle) * magnitude;

    return { x: newX, y: newY };
}

/*
function addVectors(...vectors) {
    return vectors.reduce((a, b) => ({ x: a.x + b.x, y: a.y + b.y }));
}

function matrixMult(a, b) {
    const result = [];

    for (let i = 0; i < a.length; i++) {
        result[i] = [];
        for (let j = 0; j < b[0].length; j++) {
            let sum = 0;
            for (let k = 0; k < a[0].length; k++) {
                sum += a[i][k] * b[k][j];
            }
            result[i][j] = sum;
        }
    }

    return result;
}
*/