constructor(container: HTMLElement, viewSize: [number, number]) {
// Internal UI state
this._viewSize = viewSize;
this._container = container;
this._canvasSize = [viewSize[0] / 2, viewSize[1]];
this._canvasBounds = new Rect(
Coords2d.fromXY(0, this._canvasSize[1]),
OffsetCoords2d.fromDxDy(this._canvasSize[0], -this._canvasSize[1])
);
this._needsRedraw = false;
this.gluingBounds = Rect.fromDimensions(2, 2);
this.editMode = 'triangle';
// Internal array to store the embedded 3-d triangles.
this._distance = 3;
this._triangle = Triangle2d.fromCoords(
Coords2d.origin(),
Coords2d.fromXY(1, 0),
Coords2d.fromXY(0.5, Math.sqrt(3)/4)
);
this._rotation = Quaternion.fromReal(1);
this._gluing = TriangleTetraGluing.fromEdgeIndexAndGluePoint(0, 0);
this._refreshEmbedding();
}
export function TriangleForApex(apex: Coords2d): Triangle2d {
return Triangle2d.fromCoords(
Coords2d.origin(),
Coords2d.fromXY(1, 0),
apex
);
}
export function ApexForBaseAngles(a0: number, a1: number): Coords2d {
let leftTangent =
OffsetCoords2d.fromPolar(1, a0).rootedAtCoords(Coords2d.origin());
let rightTangent = OffsetCoords2d.fromPolar(1, Math.PI - a1)
.rootedAtCoords(Coords2d.fromXY(1, 0));
return leftTangent.intersectionWith(rightTangent);
}
export function PathMargin (
triangle: Triangle2d, edgeSequence: Array<number>): number {
let tri = triangle.copy();
let leftBoundary = [];
let rightBoundary = [];
let prevEdge = 0;
for (let i = 0; i < edgeSequence.length; i++) {
let edgeDelta = (edgeSequence[i] - (prevEdge + 1) + 3) % 3; // always 0 or 1
if (edgeDelta == i % 2) {
// Right
leftBoundary.push(tri.vertex(edgeSequence[i] + 1 - (i % 2)));
} else {
// Left
rightBoundary.push(tri.vertex(edgeSequence[i] + (i % 2)));
}
tri.reflectThroughEdge(edgeSequence[i]);
prevEdge = edgeSequence[i];
}
let offset = tri.vertexCoords[0]
.asOffsetFrom(triangle.vertexCoords[0]);
let lineCoeff = OffsetCoords2d.fromDxDy(-offset.dy, offset.dx).normalized();
let o = Coords2d.origin();
let minLeft = lineCoeff.dot(triangle.vertexCoords[0].asOffsetFrom(o));
for (let i = 0; i < leftBoundary.length; i++) {
let coeff = lineCoeff.dot(leftBoundary[i].asOffsetFrom(o));
if (coeff < minLeft) {
minLeft = coeff;
}
}
let maxRight = lineCoeff.dot(triangle.vertexCoords[1].asOffsetFrom(o));
for (let i = 0; i < rightBoundary.length; i++) {
let coeff = lineCoeff.dot(rightBoundary[i].asOffsetFrom(o));
if (coeff > maxRight) {
maxRight = coeff;
}
}
//window.console.log(`${minLeft}, ${maxRight}`);
return minLeft - maxRight;
}
constructor (target: RenderTarget) {
this.target = target;
this.modelBounds = AxisRect.fromCenterAndDimensions(
Coords2d.origin(), 2, 2);
this.backgroundColor = "white";
}
static fromDimensions (width: number, height: number): Rect {
return Rect.fromCenterAndDimensions(Coords2d.origin(), width, height);
}
// @flow
import { ElementsModel } from 'faec/elements_model';
import { Coords2d, OffsetCoords2d } from 'faec/geometry';
import { AxisRect } from 'faec/polygon';
import { Line, Renderable } from 'faec/element_render';
let squareRoot = Math.sqrt(3);
let fourthRoot = Math.sqrt(squareRoot);
// (w, h) are the dimensions of the unit-area equilateral triangle
// with its base aligned with the x axis.
let triWidth = 2 / fourthRoot;
let triHeight = fourthRoot;
let triVerts = [
Coords2d.origin(),
Coords2d.fromXY(triWidth, 0),
Coords2d.fromXY(triWidth / 2, triHeight)];
let triLeft = Coords2d.midpoint(triVerts[0], triVerts[2]);
let triRight = Coords2d.midpoint(triVerts[1], triVerts[2]);
// The horizontal width of the long diagonal, which goes from
// triRight to the base and has length 1.
let diagonalWidth = Math.sqrt(1.0 - triRight.y * triRight.y);
let diagonal = OffsetCoords2d.fromDxDy(diagonalWidth, triRight.y);
let triBase = [
Coords2d.fromXY(triRight.x - diagonalWidth, 0),
Coords2d.fromXY((triRight.x - diagonalWidth) * 2, 0),
Coords2d.fromXY((triRight.x - diagonalWidth) + triWidth/2, 0)];
// The offset of the center base point from the geometric center
// Triangle: the triangle in which we're looking at billiards.
get triangle (): Triangle2d {
return Triangle2d.fromCoords(
Coords2d.origin(),
Coords2d.fromXY(1, 0),
this._apex);
}