1 | /*
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2 | * I need to do the following:
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3 | * diff angles between vectors
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4 | * find perpendicular vector to a point on a path
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5 | * find tangent to a point on a path
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6 | * transform (translate, rotate) for nodes and edges
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7 | * es modules so I can pull out just what I need
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8 | *
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9 | * Specs to compare:
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10 | * tests
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11 | * typescript
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12 | * maintained (open issues unresolved for a long time?)
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13 | * node and browser
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14 | */
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15 | import { assign as assignM } from "lodash";
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16 | import { fromPairs, isFinite, isUndefined, last, toPairs } from "lodash/fp";
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17 | import { degreesToRadians, distance, fromSlope, normalize } from "./spinoffs/Angle";
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18 | import { position } from "points";
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19 | // TODO why doesn't the following work?
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20 | // Also, why doesn't ../node_modules/kaavio/lib/drawers/edges/ exist?
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21 | //import * as edgeDrawers from "kaavio/src/drawers/edges/index";
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22 | //import * as edgeDrawers from "../node_modules/kaavio/src/drawers/edges/index";
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23 | //import * as edgeDrawers from "kaavio/src/drawers/edges/index";
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24 | //import * as edgeDrawers from "kaavio/lib/drawers/edges/index";
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25 | import * as edgeDrawers from "./edge/edgeDrawers";
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26 | // We are using the standard SVG coordinate system where:
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27 | // the origin is the upper-left-most point
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28 | // positive x is to the right
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29 | // positive y is down
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30 | // uses left hand rule, so positive angle is clockwise,
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31 | // starting with 0 pointing to the right
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32 | // The orientation is a unit vector that indicates the orientation of an
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33 | // at a point. When it is attached to a rectangle, we almost always want it to
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34 | // point away from the side to which it is attached.
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35 | export const START_SIDE_TO_ORIENTATION_MAP = {
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36 | right: [1, 0],
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37 | bottom: [0, 1],
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38 | left: [-1, 0],
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39 | top: [0, -1]
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40 | };
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41 | export const START_SIDE_TO_EMANATION_ANGLE_MAPPINGS = fromPairs(toPairs(START_SIDE_TO_ORIENTATION_MAP).map(function ([startSide, orientation]) {
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42 | return [startSide, fromSlope([0, 0], orientation)];
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43 | }));
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44 | export const EMANATION_ANGLE_TO_START_SIDE_MAPPINGS = toPairs(START_SIDE_TO_EMANATION_ANGLE_MAPPINGS).reduce(function (acc, [side, angle]) {
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45 | acc.set(angle, side);
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46 | return acc;
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47 | }, new Map());
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48 | export const START_SEGMENT_DETAILS_MAPS = toPairs(START_SIDE_TO_ORIENTATION_MAP).map(function ([startSide, orientation]) {
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49 | const [orientationX, orientationY] = orientation;
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50 | return {
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51 | sideAttachedTo: startSide,
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52 | orientation: orientation,
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53 | angle: normalize(Math.atan2(orientationY, orientationX))
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54 | };
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55 | });
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56 | export class SmartPoint {
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57 | //orientationVector?: SmartVector;
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58 | constructor(point) {
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59 | this.angle = () => {
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60 | return fromSlope([0, 0], this.orientation);
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61 | };
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62 | this.fromArray = ([x, y]) => {
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63 | this.x = x;
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64 | this.y = y;
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65 | };
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66 | this.toArray = () => {
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67 | return [this.x, this.y];
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68 | };
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69 | assignM(this, point);
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70 | /*
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71 | if (!isUndefined(this.orientation)) {
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72 | this.orientationVector = new SmartVector(
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73 | { x: 0, y: 0 },
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74 | { x: this.orientation[0], y: this.orientation[1] }
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75 | );
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76 | }
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77 | //*/
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78 | }
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79 | }
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80 | export class SmartVector {
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81 | constructor(p0, p1) {
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82 | this.angleDistance = vector2 => {
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83 | return distance(this.angle, vector2.angle);
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84 | };
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85 | this.p0 = new SmartPoint(p0);
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86 | this.p1 = new SmartPoint(p1);
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87 | this.angle = fromSlope(this.p0.toArray(), this.p1.toArray());
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88 | }
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89 | }
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90 | export class SmartPath {
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91 | constructor(points, edge) {
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92 | this.position = (scalar, accuracy) => {
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93 | const { x, y, angle: degreesFromNorth } = position(this.path.points, scalar, accuracy);
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94 | /* the points library returns the angle from north, in degrees, increasing CW, so
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95 | * this has an angle of 0 deg.:
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96 | *
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97 | * ^
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98 | * |
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99 | * |
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100 | * |
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101 | *
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102 | * and this has an angle of 90 deg.:
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103 | *
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104 | * ------->
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105 | */
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106 | return {
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107 | x,
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108 | y,
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109 | // convert to radians and use angle orientation of SVG coordinate system
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110 | angle: normalize(degreesToRadians(degreesFromNorth + 270))
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111 | };
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112 | };
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113 | const smartPoints = points.map(point => new SmartPoint(point));
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114 | this.points = smartPoints;
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115 | this.sum = new SmartVector(smartPoints[0], last(smartPoints));
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116 | if (!isUndefined(edge)) {
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117 | const { points, markerStart, markerEnd } = edge;
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118 | this.path = new edgeDrawers[edge.drawAs](smartPoints, markerStart, markerEnd);
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119 | }
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120 | }
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121 | }
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122 | // TODO explore using the packages points and angles (and maybe vectory) together
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123 | const smartPath1 = new SmartPath([
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124 | { x: 50, y: 30, moveTo: true },
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125 | { x: 50, y: 70, curve: { type: "arc", rx: 20, ry: 20, sweepFlag: 1 } },
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126 | { x: 150, y: 100, curve: { type: "arc", rx: 20, ry: 20, sweepFlag: 1 } }
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127 | ]);
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128 | const smartPath2 = new SmartPath([
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129 | { x: 100, y: 50, moveTo: true },
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130 | { x: 50, y: 70, curve: { type: "arc", rx: 20, ry: 20, sweepFlag: 1 } }
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131 | //{ x: 200, y: 100 }
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132 | ]);
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133 | /* OLD CODE BELOW */
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134 | export function addAngles(angle1, angle2) {
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135 | const sum = angle1 + angle2;
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136 | const singleRevolutionSum = sum % (2 * Math.PI);
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137 | return Math.sign(singleRevolutionSum) === -1
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138 | ? 2 * Math.PI + singleRevolutionSum
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139 | : singleRevolutionSum;
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140 | }
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141 | // see https://gist.github.com/ahwolf/4349166 and
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142 | // http://www.blackpawn.com/texts/pointinpoly/default.html
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143 | export function crossProduct(u, v) {
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144 | return u[0] * v[1] - v[0] * u[1];
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145 | }
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146 | export function flipOrientation(orientation) {
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147 | return orientation.map(orientationScalar => -1 * orientationScalar);
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148 | }
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149 | export function flipSide(side) {
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150 | return EMANATION_ANGLE_TO_START_SIDE_MAPPINGS.get(reverseAngle(START_SIDE_TO_EMANATION_ANGLE_MAPPINGS[side]));
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151 | }
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152 | export function getMinimumAngleBetweenVectors(vectorDirectionAngle1, vectorDirectionAngle2) {
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153 | const vectors = [vectorDirectionAngle1, vectorDirectionAngle2];
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154 | const minVector = Math.min.apply(undefined, vectors);
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155 | const maxVector = Math.max.apply(undefined, vectors);
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156 | if (minVector < 0 || maxVector >= 2 * Math.PI) {
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157 | throw new Error(`getMinimumAngleBetweenVectors(${vectorDirectionAngle1}, ${vectorDirectionAngle2})
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158 | inputs must be in interval [0, 2 * Math.PI).`);
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159 | }
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160 | return (Math.max(vectorDirectionAngle1, vectorDirectionAngle2) -
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161 | Math.min(vectorDirectionAngle1, vectorDirectionAngle2));
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162 | /*
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163 | const diff = addAngles(vectorDirectionAngle1, -1 * vectorDirectionAngle2);
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164 | return diff <= Math.PI ? diff : diff % Math.PI;
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165 | //*/
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166 | //return diff > Math.PI ? diff - Math.PI : diff;
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167 | }
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168 | export function getAngleOfEmanationFromPoint(point) {
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169 | const [orientationX, orientationY] = point.orientation;
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170 | return Math.atan2(orientationY, orientationX);
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171 | }
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172 | export function reverseAngle(angle) {
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173 | return addAngles(angle, Math.PI);
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174 | }
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175 | export function getAngleAtPoint(edge, positionX) {
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176 | const { id, points, markerStart, markerEnd } = edge;
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177 | const referencedPath = new edgeDrawers[edge.drawAs.toLowerCase()](points, markerStart, markerEnd);
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178 | const tangentLength = 0.02;
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179 | const firstPointOfTangent = referencedPath.getPointAtPosition(Math.max(0, positionX - tangentLength / 2));
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180 | const lastPointOfTangent = referencedPath.getPointAtPosition(Math.min(1, positionX + tangentLength / 2));
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181 | return getAngleFromPointToPoint(firstPointOfTangent, lastPointOfTangent);
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182 | }
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183 | export function getAngleFromPointToPoint({ x: x0, y: y0 }, { x: x1, y: y1 }) {
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184 | return Math.atan2(y1 - y0, x1 - x0);
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185 | }
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186 | export function getStartSideByOrientation([orientationX, orientationY]) {
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187 | if (Math.abs(orientationX) > Math.abs(orientationY)) {
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188 | if (orientationX > 0) {
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189 | return "right"; //East
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190 | }
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191 | else {
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192 | return "left"; //West
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193 | }
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194 | }
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195 | else {
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196 | if (orientationY > 0) {
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197 | return "bottom"; //South
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198 | }
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199 | else {
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200 | return "top"; //North
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201 | }
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202 | }
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203 | }
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204 | // see http://blog.acipo.com/matrix-inversion-in-javascript/
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205 | /**
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206 | * Calculate the inverse matrix.
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207 | * @returns {Matrix}
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208 | */
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209 | export function invertMatrix(M) {
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210 | // I use Guassian Elimination to calculate the inverse:
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211 | // (1) 'augment' the matrix (left) by the identity (on the right)
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212 | // (2) Turn the matrix on the left into the identity by elemetry row ops
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213 | // (3) The matrix on the right is the inverse (was the identity matrix)
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214 | // There are 3 elemtary row ops: (I combine b and c in my code)
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215 | // (a) Swap 2 rows
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216 | // (b) Multiply a row by a scalar
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217 | // (c) Add 2 rows
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218 | //if the matrix isn't square: exit (error)
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219 | if (M.length !== M[0].length) {
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220 | return;
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221 | }
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222 | //create the identity matrix (I), and a copy (C) of the original
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223 | var i = 0, ii = 0, j = 0, dim = M.length, e = 0, t = 0;
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224 | var I = [], C = [];
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225 | for (i = 0; i < dim; i += 1) {
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226 | // Create the row
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227 | I[I.length] = [];
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228 | C[C.length] = [];
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229 | for (j = 0; j < dim; j += 1) {
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230 | //if we're on the diagonal, put a 1 (for identity)
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231 | if (i === j) {
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232 | I[i][j] = 1;
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233 | }
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234 | else {
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235 | I[i][j] = 0;
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236 | }
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237 | // Also, make the copy of the original
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238 | C[i][j] = M[i][j];
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239 | }
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240 | }
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241 | // Perform elementary row operations
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242 | for (i = 0; i < dim; i += 1) {
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243 | // get the element e on the diagonal
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244 | e = C[i][i];
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245 | // if we have a 0 on the diagonal (we'll need to swap with a lower row)
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246 | if (e === 0) {
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247 | //look through every row below the i'th row
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248 | for (ii = i + 1; ii < dim; ii += 1) {
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249 | //if the ii'th row has a non-0 in the i'th col
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250 | if (C[ii][i] !== 0) {
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251 | //it would make the diagonal have a non-0 so swap it
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252 | for (j = 0; j < dim; j++) {
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253 | e = C[i][j]; //temp store i'th row
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254 | C[i][j] = C[ii][j]; //replace i'th row by ii'th
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255 | C[ii][j] = e; //repace ii'th by temp
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256 | e = I[i][j]; //temp store i'th row
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257 | I[i][j] = I[ii][j]; //replace i'th row by ii'th
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258 | I[ii][j] = e; //repace ii'th by temp
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259 | }
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260 | //don't bother checking other rows since we've swapped
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261 | break;
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262 | }
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263 | }
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264 | //get the new diagonal
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265 | e = C[i][i];
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266 | //if it's still 0, not invertable (error)
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267 | if (e === 0) {
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268 | return;
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269 | }
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270 | }
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271 | // Scale this row down by e (so we have a 1 on the diagonal)
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272 | for (j = 0; j < dim; j++) {
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273 | C[i][j] = C[i][j] / e; //apply to original matrix
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274 | I[i][j] = I[i][j] / e; //apply to identity
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275 | }
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276 | // Subtract this row (scaled appropriately for each row) from ALL of
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277 | // the other rows so that there will be 0's in this column in the
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278 | // rows above and below this one
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279 | for (ii = 0; ii < dim; ii++) {
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280 | // Only apply to other rows (we want a 1 on the diagonal)
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281 | if (ii === i) {
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282 | continue;
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283 | }
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284 | // We want to change this element to 0
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285 | e = C[ii][i];
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286 | // Subtract (the row above(or below) scaled by e) from (the
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287 | // current row) but start at the i'th column and assume all the
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288 | // stuff left of diagonal is 0 (which it should be if we made this
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289 | // algorithm correctly)
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290 | for (j = 0; j < dim; j++) {
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291 | C[ii][j] -= e * C[i][j]; //apply to original matrix
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292 | I[ii][j] -= e * I[i][j]; //apply to identity
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293 | }
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294 | }
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295 | }
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296 | //we've done all operations, C should be the identity
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297 | //matrix I should be the inverse:
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298 | return I;
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299 | }
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300 | // from http://tech.pro/tutorial/1527/matrix-multiplication-in-functional-javascript
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301 | export function multiplyMatrices(m1, m2) {
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302 | var result = [];
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303 | for (var i = 0; i < m1.length; i++) {
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304 | result[i] = [];
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305 | for (var j = 0; j < m2[0].length; j++) {
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306 | var sum = 0;
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307 | for (var k = 0; k < m1[0].length; k++) {
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308 | sum += m1[i][k] * m2[k][j];
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309 | }
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310 | result[i][j] = sum;
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311 | }
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312 | }
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313 | return result;
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314 | }
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315 | /**
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316 | * rotate
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317 | *
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318 | * @param theta (float): rotation angle in radians, measured clockwise
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319 | * @return transformation matrix for rotation
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320 | *
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321 | * Note that for Canvas and SVG, the y axis points down:
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322 | *
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323 | * *---------> x
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324 | * |
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325 | * |
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326 | * |
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327 | * v
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328 | *
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329 | * y
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330 | *
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331 | * The transformation matrix returned takes this into account and is intentionally
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332 | * different from the transformation matrix that would be returned if the y-axis
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333 | * pointed up, as is common in many math classes.
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334 | */
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335 | export function rotate(theta) {
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336 | if (!isFinite(theta)) {
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337 | throw new Error(`Invalid input: rotate(${theta}). Requires a finite number.`);
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338 | }
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339 | return [
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340 | [Math.cos(theta), -1 * Math.sin(theta), 0],
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341 | [Math.sin(theta), Math.cos(theta), 0],
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342 | [0, 0, 1]
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343 | ];
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344 | }
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345 | export function scale([xScale, yScale]) {
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346 | if (!isFinite(xScale) || !isFinite(yScale)) {
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347 | throw new Error(`Invalid input: rotate([${xScale}, ${yScale}]). Requires array of two finite numbers.`);
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348 | }
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349 | return [[xScale, 0, 0], [0, yScale, 0], [0, 0, 1]];
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350 | }
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351 | export function translate([xTranslation, yTranslation]) {
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352 | if (!isFinite(xTranslation) || !isFinite(yTranslation)) {
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353 | throw new Error(`Invalid input: translate([${xTranslation}, ${yTranslation}]). Requires array of two finite numbers.`);
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354 | }
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355 | return [[1, 0, xTranslation], [0, 1, yTranslation], [0, 0, 1]];
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356 | }
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357 | const transformations = {
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358 | rotate,
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359 | scale,
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360 | translate
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361 | };
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362 | export function getTransformationMatrix(transformationSequence) {
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363 | // Start with identity matrix
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364 | var concatenatedTransformationMatrix = [[1, 0, 0], [0, 1, 0], [0, 0, 1]];
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365 | transformationSequence.forEach(function (transformation) {
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366 | var thisTransformationMatrix = transformations[transformation.key](transformation.value);
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367 | concatenatedTransformationMatrix = multiplyMatrices(concatenatedTransformationMatrix, thisTransformationMatrix);
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368 | });
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369 | return concatenatedTransformationMatrix;
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370 | }
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371 | export function multiplyMatrixByVector(transformationMatrix, vector) {
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372 | var x = vector[0][0] * transformationMatrix[0][0] +
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373 | vector[1][0] * transformationMatrix[0][1] +
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374 | vector[2][0] * transformationMatrix[0][2], y = vector[0][0] * transformationMatrix[1][0] +
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375 | vector[1][0] * transformationMatrix[1][1] +
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376 | vector[2][0] * transformationMatrix[1][2], z = vector[0][0] * transformationMatrix[2][0] +
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377 | vector[1][0] * transformationMatrix[2][1] +
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378 | vector[2][0] * transformationMatrix[2][2];
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379 | return [[x], [y], [z]];
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380 | }
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381 | /**
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382 | * sameSide
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383 | *
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384 | * Calculate whether the current edge's second point, a, (end of first segment)
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385 | * and its final point, b, are both on the same side of the referenced edge.
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386 | *
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387 | * current edge: pipes/hyphens
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388 | * referenced edge: dots
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389 | *
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390 | * Example of True
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391 | *
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392 | * p1
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393 | * .
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394 | * .
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395 | * *------------a
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396 | * . |
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397 | * . |
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398 | * . |
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399 | * . |
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400 | * . |
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401 | * . |
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402 | * . |
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403 | * . |
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404 | * . |
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405 | * . |
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406 | * . *-----b
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407 | * .
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408 | * .
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409 | * p2
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410 | *
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411 | *
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412 | * Example of False
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413 | *
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414 | * p1
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415 | * .
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416 | * *------------a
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417 | * . |
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418 | * . |
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419 | * . |
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420 | * . |
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421 | * . |
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422 | * .|
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423 | * |.
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424 | * | .
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425 | * | .
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426 | * | .
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427 | * *-----b .
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428 | * .
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429 | * p2
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430 | *
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431 | *
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432 | * @param {Object} p1 - first point of the referenced edge
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433 | * @param {Object} p2 - last point of the referenced edge
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434 | * @param {Object} a - last point of the first segment of the current edge (the point following the start point)
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435 | * @param {Object} b - point where the current edge ends
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436 | * @return {Boolean) - whether the last point of the first segment of the current edge is on the same side as the last point of the current edge
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437 | */
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438 | export function sameSide(p1, p2, a, b) {
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439 | const bMinusA = [b.x - a.x, b.y - a.y];
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440 | const p1MinusA = [p1.x - a.x, p1.y - a.y];
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441 | const p2MinusA = [p2.x - a.x, p2.y - a.y];
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442 | const crossProduct1 = crossProduct(bMinusA, p1MinusA);
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443 | const crossProduct2 = crossProduct(bMinusA, p2MinusA);
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444 | return Math.sign(crossProduct1) === Math.sign(crossProduct2);
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445 | }
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446 | export function transform({ element, transformOrigin, transformationSequence }) {
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447 | const { x, y, width, height } = element;
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448 | (transformOrigin = transformOrigin || "50% 50%"),
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449 | (transformationSequence = transformationSequence || []);
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450 | var transformOriginKeywordMappings = {
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451 | left: "0%",
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452 | center: "50%",
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453 | right: "100%",
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454 | top: "0%",
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455 | bottom: "100%"
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456 | };
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457 | var transformOriginKeywordMappingsKeys = Object.keys(transformOriginKeywordMappings);
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458 | var transformOriginPoint = transformOrigin
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459 | .split(" ")
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460 | .map(function (value, i) {
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461 | let numericOrPctValue;
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462 | let numericValue;
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463 | if (transformOriginKeywordMappingsKeys.indexOf(value) > -1) {
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464 | numericOrPctValue = transformOriginKeywordMappings[value];
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465 | }
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466 | else {
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467 | numericOrPctValue = value;
|
468 | }
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469 | if (numericOrPctValue.indexOf("%") > -1) {
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470 | var decimalPercent = parseFloat(numericOrPctValue) / 100;
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471 | if (i === 0) {
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472 | numericValue = decimalPercent * width;
|
473 | }
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474 | else {
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475 | numericValue = decimalPercent * height;
|
476 | }
|
477 | }
|
478 | else if (value.indexOf("em") > -1) {
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479 | // TODO refactor. this is hacky.
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480 | numericValue = parseFloat(numericOrPctValue) * 12;
|
481 | }
|
482 | else {
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483 | numericValue = parseFloat(numericOrPctValue);
|
484 | }
|
485 | if (i === 0) {
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486 | numericValue += x;
|
487 | }
|
488 | else {
|
489 | numericValue += y;
|
490 | }
|
491 | return numericValue;
|
492 | });
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493 | // shift origin from top left corner of element bounding box to point specified by transformOrigin (default: center of bounding box)
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494 | transformationSequence.unshift({
|
495 | key: "translate",
|
496 | value: [transformOriginPoint[0], transformOriginPoint[1]]
|
497 | });
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498 | // shift origin back to top left corner of element bounding box
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499 | transformationSequence.push({
|
500 | key: "translate",
|
501 | value: [-1 * transformOriginPoint[0], -1 * transformOriginPoint[1]]
|
502 | });
|
503 | var transformationMatrix = getTransformationMatrix(transformationSequence);
|
504 | var topLeftPoint = [[x], [y], [1]];
|
505 | var bottomRightPoint = [[x + width], [y + height], [1]];
|
506 | var topLeftPointTransformed = multiplyMatrixByVector(transformationMatrix, topLeftPoint);
|
507 | var bottomRightPointTransformed = multiplyMatrixByVector(transformationMatrix, bottomRightPoint);
|
508 | element.x = topLeftPointTransformed[0][0];
|
509 | element.y = topLeftPointTransformed[1][0];
|
510 | element.width = bottomRightPointTransformed[0][0] - element.x;
|
511 | element.height = bottomRightPointTransformed[1][0] - element.y;
|
512 | return element;
|
513 | }
|
514 | //# 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