Press n or j to go to the next uncovered block, b, p or k for the previous block.
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| Title: PointElement.ts |
| A port of the software Geometry Applet by |
| Author: David E. Joyce |
| Department of Mathematics and Computer Science |
| Clark University |
| Worcester, MA 01610-1477 |
| U.S.A. |
| |
| http://aleph0.clarku.edu/~djoyce/home.html |
| djoyce@clarku.edu |
| |
| Date: February, 1996. Version 2.0.0 May, 1997. |
| TypeScript Port: 2019, Nelson Brown, brownnrl@gmail.com |
| https://www.nelsonbrown.net/ |
+----------------------------------------------------------------------*/
import {GeomElement} from "../GeomElement";
import {PlaneElement} from "../plane/PlaneElement";
import {CircleElement} from "../circle/CircleElement";
import {SlateCanvas} from "../../Slate";
export interface IPointElementConstruction {
x? : number;
y? : number;
z? : number;
AP? : PlaneElement;
}
export class PointElement extends GeomElement {
protected _x : number;
protected _y : number;
protected _z : number;
_AP : PlaneElement;
constructor(ip? : IPointElementConstruction) {
super();
this.dimension = 0;
this._x = ip && ip.x || 0;
this._y = ip && ip.y || 0;
this._z = ip && ip.z || 0;
this._AP = ip && ip.AP || null;
}
get x() { return this._x }
set x(value: number) { this._x = value }
get y() { return this._y }
set y(value: number) { this._y = value }
get z() { return this._z }
set z(value: number) { this._z = value }
get AP() { return this._AP; }
set AP(v : PlaneElement) { this._AP = v; }
public defined() : boolean {
return !isNaN(this._x) && !isNaN(this._y) && !isNaN(this._z)
&& this._x != null && true && this._y != null && true && this._z != null;
}
to(B : PointElement ) : PointElement {this._x = B._x; this._y = B._y; this._z= B._z; return this;}
plus(B : PointElement ) : PointElement {this._x += B._x; this._y += B._y; this._z+= B._z; return this;}
minus(B : PointElement) : PointElement {this._x -= B._x; this._y -= B._y; this._z-= B._z; return this;}
times(a : number) : PointElement {this._x *= a; this._y *= a; this._z *= a; return this;}
static difference(A : PointElement, B : PointElement) : PointElement {
return new PointElement({x:A.x-B.x, y:A.y-B.y, z:A.z-B.z, AP: null});
}
static product(a : number, B : PointElement) : PointElement {
return new PointElement({x:a*B.x, y:a*B.y, z:a*B.z, AP: null});
}
static dot(A : PointElement, B : PointElement) : number {
return A.x * B.x + A.y * B.y + A.z * B.z;
}
public length2() : number {
return this._x * this._x + this._y * this._y + this._z * this._z;
}
public length() : number {
return Math.sqrt(this.length2());
}
public distance2(B : PointElement) : number {
return (this._x-B.x)*(this._x-B.x) +
(this._y-B.y)*(this._y-B.y) +
(this._z-B.z)*(this._z-B.z);
}
public distance(B : PointElement) : number {
return Math.sqrt(this.distance2(B));
}
public toCross(A : PointElement, B : PointElement) : PointElement {
// set to the cross product of A and B
this._x = A.y*B.z - A.z*B.y;
this._y = A.z*B.x - A.x*B.z;
this._z = A.x*B.y - A.y*B.x;
return this;
}
public static cross(A: PointElement, B: PointElement) : PointElement {
// return the cross product of A and B
return new PointElement({x: A.y*B.z - A.z*B.y,
y: A.z*B.x - A.x*B.z,
z: A.x*B.y - A.y*B.x,
AP: null});
}
public static triple(A: PointElement, B: PointElement, C: PointElement) : number {
// return the triple product of A, B, and C
return A.x*(B.y*C.z - B.z*C.y) +
B.x*(C.y*A.z - C.z*A.y) +
C.x*(A.y*B.z - A.z*B.y);
}
toLine(A: PointElement, B: PointElement, segment: boolean) : PointElement{
/*---------------------------------------------------------------------+
| Project this point to the foot of the perpendicular from it to the |
| line determined by the points A and B. If A were the origin, then |
| the foot would be at ((this dot B)/B^2) B. When segment is true |
| and the foot is beyond A or B, then move the point to the closer |
| of A and B. |
+---------------------------------------------------------------------*/
let V : PointElement = PointElement.difference(B,A);
this.minus(A);
let factor : number= PointElement.dot(V,this)/V.length2();
if (segment) {
if (factor < 0.0) factor = 0.0;
else if (factor > 1.0) factor = 1.0;
}
V.times(factor);
return this.to(V).plus(A);
}
public toPlane (P : PlaneElement) : PointElement {
/*---------------------------------------------------------------------+
| Project this point to the foot of the perpendicular from it to the |
| plane P. |
+---------------------------------------------------------------------*/
if (P.isScreen) {
this._z = 0.0;
} else {
this.minus(P.A);
let s : number = PointElement.dot(this, P.S);
let t = PointElement.dot(this, P.T);
this.to(P.S).times(s).plus(PointElement.product(t,P.T)).plus(P.A);
}
return this;
}
uptoPlane(P : PlaneElement) : PointElement {
/*---------------------------------------------------------------------+
| Project this point to the point on the plane P where the vertical |
| line through this meets P. |
+---------------------------------------------------------------------*/
if (P.isScreen) {
this._z = 0.0;
} else {
this.minus(P.A);
let den : number = P.S.x*P.T.y - P.S.y*P.T.x;
let s : number = (this.x*P.T.y - this.y*P.T.x) / den;
let t : number = (this.y*P.S.x - this.x*P.S.y) / den;
this.to(P.S).times(s).plus(PointElement.product(t,P.T)).plus(P.A);
}
return this;
}
toCircumcenter (A: PointElement, B: PointElement, C: PointElement) : PointElement{
/*---------------------------------------------------------------------+
| Move this point to the center of the circle passing through the |
| points A, B, and C. |
+---------------------------------------------------------------------*/
if (A.z == 0.0 && B.z == 0.0 && C.z == 0.0) {
let u : number = ((A.x-B.x)*(A.x+B.x) + (A.y-B.y)*(A.y+B.y)) / 2.0;
let v : number = ((B.x-C.x)*(B.x+C.x) + (B.y-C.y)*(B.y+C.y)) / 2.0;
let den : number = (A.x-B.x)*(B.y-C.y) - (B.x-C.x)*(A.y-B.y);
this._x = (u * (B.y-C.y) - v*(A.y-B.y)) / den;
this._y = (v * (A.x-B.x) - u*(B.x-C.x)) / den;
this._z = 0.0;
} else {
let BmA : PointElement = PointElement.difference(B,A)
let CmA : PointElement = PointElement.difference(C,A);
let BC : number = PointElement.dot(BmA,CmA);
let B2 : number = BmA.length2();
let C2 : number = CmA.length2();
//double BC2 = BC*BC;
let den : number = 2.0*(B2*C2-BC*BC);
let s : number = C2*(B2-BC)/den;
let t : number = B2*(C2-BC)/den;
this.to(A).plus(BmA.times(s)).plus(CmA.times(t));
}
return this;
}
toCircle (C: CircleElement) : PointElement {
/*---------------------------------------------------------------------+
| Move this point to the nearest point on the circle C. |
+---------------------------------------------------------------------*/
if (C.AP.isScreen) {
let factor : number = C.radius / this.distance(C.Center);
this._x = C.Center.x + factor*(this._x - C.Center.x);
this._y = C.Center.y + factor*(this._y - C.Center.y);
this._z = 0.0;
} else { // 3d case: project to plane of circle then move to sphere of circle
this.toPlane(C.AP);
this.toSphere(C.Center,C.radius);
}
return this;
}
toSphere (Center : PointElement, radius : number) : PointElement{
/*---------------------------------------------------------------------+
| Move this point to the nearest point on the sphere S. |
+---------------------------------------------------------------------*/
let factor : number = radius / this.distance(Center);
this._x = Center.x + factor*(this._x - Center.x);
this._y = Center.y + factor*(this._y - Center.y);
this._z = Center.z + factor*(this._z - Center.z);
return this;
}
public static area(A: PointElement, B: PointElement, C: PointElement) {
// return the area of the triangle ABC
let U : PointElement = PointElement.difference(B,A);
let V : PointElement = PointElement.difference(C,A);
return this.cross(U,V).length()/2.0;
}
public angle(B: PointElement, C: PointElement, P: PlaneElement) : number {
// Determine the angle BAC in the plane P where this is A.
// The angle lies between -pi and pi (-180 degrees and 180 degrees)
let Bx : number = B.x - this._x, Cx = C.x - this._x;
let By : number = B.y - this._y, Cy = C.y - this._y;
if (P.isScreen) {
return Math.atan2 (Bx*Cy - By*Cx, Bx*Cx + By*Cy);
} else { // 3d case. First get P-coordinates for B and C
let Bz : number = B.z -this._z, Cz = C.z -this._z;
let Bs : number = Bx * P.S.x + By * P.S.y + Bz * P.S.z;
let Bt : number = Bx * P.T.x + By * P.T.y + Bz * P.T.z;
let Cs : number = Cx * P.S.x + Cy * P.S.y + Cz * P.S.z;
let Ct : number = Cx * P.T.x + Cy * P.T.y + Cz * P.T.z;
return Math.atan2(Bs * Ct - Bt * Cs, Bs * Cs + Bt * Ct);
}
}
toIntersection (
A: PointElement,
B: PointElement,
C: PointElement,
D: PointElement,
P: PlaneElement) : PointElement {
if (P.isScreen) {
// move this point to where the two lines AB and CD meet
let d0 : number = A.x*B.y - A.y*B.x;
let d1 : number = C.x*D.y - C.y*D.x;
let den : number = (B.y-A.y)*(C.x-D.x) - (A.x-B.x)*(D.y-C.y);
this._x = (d0*(C.x-D.x) - d1*(A.x-B.x)) / den;
this._y = (d1*(B.y-A.y) - d0*(D.y-C.y)) / den;
} else { // 3d case
let AmA : PointElement = PointElement.difference(A,P.A);
let BmA : PointElement = PointElement.difference(B,P.A);
let CmA : PointElement = PointElement.difference(C,P.A);
let DmA : PointElement = PointElement.difference(D,P.A);
let Ax = PointElement.dot(AmA,P.S);
let Ay = PointElement.dot(AmA,P.T);
let Bx = PointElement.dot(BmA,P.S);
let By = PointElement.dot(BmA,P.T);
let Cx = PointElement.dot(CmA,P.S);
let Cy = PointElement.dot(CmA,P.T);
let Dx = PointElement.dot(DmA,P.S);
let Dy = PointElement.dot(DmA,P.T);
let d0 = Ax*By - Ay*Bx;
let d1 = Cx*Dy - Cy*Dx;
let den = (By-Ay)*(Cx-Dx) - (Ax-Bx)*(Dy-Cy);
let s = (d0*(Cx-Dx) - d1*(Ax-Bx)) / den;
let t = (d1*(By-Ay) - d0*(Dy-Cy)) / den;
this.to(P.S).times(s).plus(PointElement.product(t,P.T)).plus(P.A);
}
return this;
}
toIntersectionPL (
P: PlaneElement,
D: PointElement,
E: PointElement) : PointElement {
// move this point to where the plane P meets the line DE
this.to(E).minus(D);
let DmA : PointElement = PointElement.difference(D,P.A);
let u : number = -PointElement.triple(P.S,P.T,DmA)
/ PointElement.triple(P.S,P.T,this);
return this.times(u).plus(D);
}
toInvertPoint (A: PointElement, C: CircleElement) : PointElement {
// move this point to the inversion of the point A in the circle C
let factor : number = C.radius2 / A.distance2(C.Center);
return this.to(A).minus(C.Center).times(factor).plus(C.Center);
}
toSimilar (
A: PointElement,
B: PointElement,
P : PlaneElement,
D: PointElement,
E: PointElement,
F: PointElement,
Q: PlaneElement) : PointElement {
// move this point to the location C so that triangle ABC is similar
// to triangle DEF.
let theta : number = D.angle(E,F,Q);
let co : number = Math.cos(theta), si : number = Math.sin(theta);
let factor : number = D.distance(F) / D.distance(E);
if (P.isScreen) {
this._x = B.x;
this._y = B.y;
this.rotate(A,co,si,P);
this._x = A.x + factor*(this._x - A.x);
this._y = A.y + factor*(this._y - A.y);
this._z = 0.0;
} else {
let BmA : PointElement = PointElement.difference(B,A);
let s : number = PointElement.dot(BmA,P.S);
let t : number = PointElement.dot(BmA,P.T);
let ss : number = factor*(co*s - si*t);
let tt : number = factor*(si*s + co*t);
this._x = ss*P.S.x + tt*P.T.x + A.x;
this._y = ss*P.S.y + tt*P.T.y + A.y;
this._z = ss*P.S.z + tt*P.T.z + A.z;
}
return this;
}
public rotate ( pivot : PointElement,
ac : number,
as : number,
plane?: PlaneElement) : void {
/*--------------------------------------------------------------------------+
| Scale and rotate this point around the axis through the pivot and |
| perpendicular to the plane. Scale by a factor of a, and rotate by the |
| angle theta where ac = a cos theta, and as = a sin theta. |
+--------------------------------------------------------------------------*/
if (plane == null) plane = pivot._AP;
if (this == pivot) return;
if (plane.isScreen) {
let dx : number = this.x - pivot.x;
let dy : number = this.y - pivot.y;
this._x = pivot.x + ac*dx - as*dy;
this._y = pivot.y + as*dx + ac*dy;
} else {
this.minus(pivot);
let S : PointElement = plane.S;
let T : PointElement = plane.T;
let U : PointElement = plane.U;
let s : number = PointElement.dot(this,S);
let t : number = PointElement.dot(this,T);
let z1 : number = PointElement.dot(this,U);
let x1 : number = ac*s - as*t;
let y1 : number = as*s + ac*t;
this._x = pivot.x + x1*S.x + y1*T.x + z1*U.x;
this._y = pivot.y + x1*S.y + y1*T.y + z1*U.y;
this._z = pivot.z + x1*S.z + y1*T.z + z1*U.z;
}
}
public drawName(c: SlateCanvas): void {
if (this.nameColor != null && this.name != null && this.defined()) {
this.drawString(Math.round(this.x), Math.round(this.y), c)
}
}
public drawVertex(c: SlateCanvas, color?: string): void {
let ctx : CanvasRenderingContext2D = c.getContext("2d") as CanvasRenderingContext2D;
if (color == null) {
if (this.shouldHighlight) {
color = this.vertexHighlightColor;
} else {
color = this.vertexColor;
}
}
if (color == null) return;
ctx.beginPath();
ctx.fillStyle = color;
ctx.arc(this._x, this._y, 2, 0, 2*Math.PI, false);
ctx.fill();
}
public translate(dx: number, dy: number): void {
this._x += dx;
this._y += dy;
}
public update(): void {
}
public drawEdge(c: SlateCanvas): void {
}
public drawFace(c: SlateCanvas): void {
}
}
|