/*
Copyright 2008-2026
Matthias Ehmann,
Michael Gerhaeuser,
Carsten Miller,
Bianca Valentin,
Alfred Wassermann,
Peter Wilfahrt
This file is part of JSXGraph.
JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
You can redistribute it and/or modify it under the terms of the
* GNU Lesser General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version
OR
* MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
JSXGraph is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License and
the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
and <https://opensource.org/licenses/MIT/>.
*/
/*global JXG: true, define: true*/
/*jslint nomen: true, plusplus: true*/
/**
* @fileoverview In this file the conic sections defined.
*/
import JXG from "../jxg.js";
import Const from "../base/constants.js";
import Coords from "../base/coords.js";
import Mat from "../math/math.js";
import Numerics from "../math/numerics.js";
import Geometry from "../math/geometry.js";
import Type from "../utils/type.js";
/**
* @class An ellipse is a special conic section given by two points (the foci) and a third point on the ellipse or
* the length of the major axis.
* @pseudo
* @name Ellipse
* @elementclass curve
* @augments JXG.Curve
* @constructor
* @type JXG.Curve
* @see Conic
* @see Hyperbola
* @see Parabola
* @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
*/
/**
* @jsxgraphsignature Ellipse
* Parent elements can be three elements either of type {@link JXG.Point} or array of
* numbers describing the coordinates of a point. In the latter case the point will be
* constructed automatically as a fixed invisible point.
*
* @param {PointLike} point1
* @param {PointLike} point2
* @param {PointLike} point3
* @param {Number} [start=0] parameter of the curve start, default: 0.
* @param {Number} [end=2π] parameter for the curve end, default: 2π.
*
* @example <caption>Create an ellipse by three points</caption>
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var C = board.create('point', [1,1]);
* var el = board.create('ellipse',[A,B,C]);
* </pre><div class="jxgbox" id="JXGa4d7fb6f-8708-4e45-87f2-2379ae2bd2c0" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function() {
* var board = JXG.JSXGraph.initBoard('JXGa4d7fb6f-8708-4e45-87f2-2379ae2bd2c0', {boundingbox:[-6,6,6,-6], keepaspectratio:true, showcopyright: false, shownavigation: false});
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var C = board.create('point', [1,1]);
* var el = board.create('ellipse',[A,B,C]);
* })();
* </script><pre>
*
* @example <caption>Create an elliptical arc</caption>
* var p1 = board.create('point', [-1, 2]);
* var p2 = board.create('point', [ 1, 2]);
* var p3 = board.create('point', [0, 3]);
*
* var ell = board.create('ellipse', [
* p1, p2, p3, 0, Math.PI], {
* lastArrow: {type: 7}
* });
*
* </pre><div id="JXG950f7c07-27a4-4c67-9505-c73c22ce9345" class="jxgbox" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function() {
* var board = JXG.JSXGraph.initBoard('JXG950f7c07-27a4-4c67-9505-c73c22ce9345',
* {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
* var p1 = board.create('point', [-1, 2]);
* var p2 = board.create('point', [ 1, 2]);
* var p3 = board.create('point', [0, 3]);
*
* var ell = board.create('ellipse', [
* p1, p2, p3, 0, Math.PI], {
* lastArrow: {type: 7}
* });
*
* })();
*
* </script><pre>
*
*/
/**
* @jsxgraphsignature Ellipse
* Parent elements can be two elements either of type {@link JXG.Point} or array of
* numbers describing the coordinates of a point.
* The third parameter is a number/function which defines the length of the major axis
* @param {PointLike} point1
* @param {PointLike} point2
* @param {NumberLike} number
* @param {Number} [start=0] parameter of the curve start, default: 0.
* @param {Number} [end=2π] parameter for the curve end, default: 2π.
*
*/
JXG.createEllipse = function (board, parents, attributes) {
var polarForm,
curve,
M,
C,
majorAxis,
i,
hasPointOrg,
// focus 1 and focus 2
F = [],
attr_foci = Type.copyAttributes(attributes, board.options, "conic", 'foci'),
attr_center = Type.copyAttributes(attributes, board.options, "conic", 'center'),
attr_curve = Type.copyAttributes(attributes, board.options, 'conic');
// The foci and the third point are either points or coordinate arrays.
for (i = 0; i < 2; i++) {
// focus i given by coordinates
if (parents[i].length > 1) {
F[i] = board.create("point", parents[i], attr_foci);
// focus i given by point
} else if (Type.isPoint(parents[i])) {
F[i] = board.select(parents[i]);
// given by function
} else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {
F[i] = parents[i]();
// focus i given by point name
} else if (Type.isString(parents[i])) {
F[i] = board.select(parents[i]);
} else {
throw new Error(
"JSXGraph: Can't create Ellipse with parent types '" +
typeof parents[0] +
"' and '" +
typeof parents[1] +
"'." +
"\nPossible parent types: [point,point,point], [point,point,number|function]"
);
}
}
// length of major axis
if (Type.isNumber(parents[2])) {
majorAxis = Type.createFunction(parents[2], board);
} else if (Type.isFunction(parents[2]) && Type.isNumber(parents[2]())) {
majorAxis = parents[2];
} else {
// point on ellipse
if (Type.isPoint(parents[2])) {
C = board.select(parents[2]);
// point on ellipse given by coordinates
} else if (parents[2].length > 1) {
C = board.create("point", parents[2], attr_foci);
// given by function
} else if (Type.isFunction(parents[2]) && Type.isPoint(parents[2]())) {
C = parents[2]();
// focus i given by point name
} else if (Type.isString(parents[2])) {
C = board.select(parents[2]);
} else {
throw new Error(
"JSXGraph: Can't create Ellipse with parent types '" +
typeof parents[0] +
"' and '" +
typeof parents[1] +
"' and '" +
typeof parents[2] +
"'." +
"\nPossible parent types: [point,point,point], [point,point,number|function]"
);
}
/** @ignore */
majorAxis = function () {
return C.Dist(F[0]) + C.Dist(F[1]);
};
}
// to
if (!Type.exists(parents[4])) {
parents[4] = 2 * Math.PI;
}
// from
if (!Type.exists(parents[3])) {
parents[3] = 0.0;
}
M = board.create(
"point",
[
function () {
return (F[0].X() + F[1].X()) * 0.5;
},
function () {
return (F[0].Y() + F[1].Y()) * 0.5;
}
],
attr_center
);
/**
* @class
* @ignore
*/
curve = board.create(
"curve",
[
function (x) {
return 0;
},
function (x) {
return 0;
},
parents[3],
parents[4]
],
attr_curve
);
curve.majorAxis = majorAxis;
// Store the original hasPoint method. It will be called inside of the new hasPoint method.
hasPointOrg = curve.hasPoint;
/** @ignore */
polarForm = function (phi, suspendUpdate) {
var r, rr, ax, ay, bx, by, axbx, ayby, f;
if (!suspendUpdate) {
r = majorAxis();
rr = r * r;
ax = F[0].X();
ay = F[0].Y();
bx = F[1].X();
by = F[1].Y();
axbx = ax - bx;
ayby = ay - by;
f = (rr - ax * ax - ay * ay + bx * bx + by * by) / (2 * r);
curve.quadraticform = [
[f * f - bx * bx - by * by, (f * axbx) / r + bx, (f * ayby) / r + by],
[(f * axbx) / r + bx, (axbx * axbx) / rr - 1, (axbx * ayby) / rr],
[(f * ayby) / r + by, (axbx * ayby) / rr, (ayby * ayby) / rr - 1]
];
}
};
/** @ignore */
curve.X = function (phi, suspendUpdate) {
var r = majorAxis(),
c = F[1].Dist(F[0]),
b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) - r),
beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());
if (!suspendUpdate) {
polarForm(phi, suspendUpdate);
}
return F[0].X() + Math.cos(beta + phi) * b;
};
/** @ignore */
curve.Y = function (phi, suspendUpdate) {
var r = majorAxis(),
c = F[1].Dist(F[0]),
b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) - r),
beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());
return F[0].Y() + Math.sin(beta + phi) * b;
};
curve.midpoint = curve.center = M;
curve.type = Const.OBJECT_TYPE_CONIC;
curve.subs = {
center: curve.center
};
curve.inherits.push(curve.center, F[0], F[1]);
if (Type.isPoint(C)) {
curve.inherits.push(C);
}
/**
* Checks whether (x,y) is near the ellipse line or inside of the ellipse
* (in case JXG.Options.conic#hasInnerPoints is true).
* @param {Number} x Coordinate in x direction, screen coordinates.
* @param {Number} y Coordinate in y direction, screen coordinates.
* @returns {Boolean} True if (x,y) is near the ellipse, False otherwise.
* @private
* @ignore
*/
curve.hasPoint = function (x, y) {
var ac, bc, r, p, dist;
if (this.evalVisProp('hasinnerpoints')) {
ac = F[0].coords;
bc = F[1].coords;
r = this.majorAxis();
p = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board);
dist = p.distance(Const.COORDS_BY_USER, ac) + p.distance(Const.COORDS_BY_USER, bc);
return dist <= r;
}
return hasPointOrg.apply(this, arguments);
};
M.addChild(curve);
for (i = 0; i < 2; i++) {
if (Type.isPoint(F[i])) {
F[i].addChild(curve);
}
}
if (Type.isPoint(C)) {
C.addChild(curve);
}
curve.setParents(parents);
return curve;
};
/**
* @class A hyperbola is a special conic section given by two points (the foci) and a third point on the hyperbola or
* the length of the major axis.
* @pseudo
* @name Hyperbola
* @elementclass curve
* @augments JXG.Curve
* @constructor
* @type JXG.Curve
* @see Conic
* @see Ellipse
* @see Parabola
* @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
*/
/**
* @jsxgraphsignature Hyperbola
* Parent elements can be three elements either of type {@link JXG.Point} or array of
* numbers describing the coordinates of a point.
* In the latter case the point will be constructed automatically as a fixed invisible point.
* @param {PointLike} point1
* @param {PointLike} point2
* @param {PointLike} point3
* @param {Number} [start=-π] parameter of the curve start, default: -π.
* @param {Number} [end=π] parameter for the curve end, default: π.
*
* @example <caption>Create an hyperbola by three points</caption>
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var C = board.create('point', [1,1]);
* var el = board.create('hyperbola',[A,B,C]);
* </pre><div class="jxgbox" id="JXGcf99049d-a3fe-407f-b936-27d76550f8c4" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function(){
* var board = JXG.JSXGraph.initBoard('JXGcf99049d-a3fe-407f-b936-27d76550f8c4', {boundingbox:[-6,6,6,-6], keepaspectratio:true, showcopyright: false, shownavigation: false});
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var C = board.create('point', [1,1]);
* var el = board.create('hyperbola',[A,B,C]);
* })();
* </script><pre>
*/
/**
* @jsxgraphsignature Hyperbola
* Parent elements can be two elements either of type {@link JXG.Point} or array of
* numbers describing the coordinates of a point.
* The third parameter is a number/function which defines the length of the major axis
* @param {PointLike} point1
* @param {PointLike} point2
* @param {NumberLike} number
* @param {Number} [start=-π] parameter of the curve start, default: -π.
* @param {Number} [end=π] parameter for the curve end, default: π.
*/
JXG.createHyperbola = function (board, parents, attributes) {
var polarForm,
curve,
M,
C,
majorAxis,
i,
// focus 1 and focus 2
F = [],
attr_foci = Type.copyAttributes(attributes, board.options, "conic", 'foci'),
attr_center = Type.copyAttributes(attributes, board.options, "conic", 'center'),
attr_curve = Type.copyAttributes(attributes, board.options, 'conic');
// The foci and the third point are either points or coordinate arrays.
for (i = 0; i < 2; i++) {
// focus i given by coordinates
if (parents[i].length > 1) {
F[i] = board.create("point", parents[i], attr_foci);
// focus i given by point
} else if (Type.isPoint(parents[i])) {
F[i] = board.select(parents[i]);
// given by function
} else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {
F[i] = parents[i]();
// focus i given by point name
} else if (Type.isString(parents[i])) {
F[i] = board.select(parents[i]);
} else {
throw new Error(
"JSXGraph: Can't create Hyperbola with parent types '" +
typeof parents[0] +
"' and '" +
typeof parents[1] +
"'." +
"\nPossible parent types: [point,point,point], [point,point,number|function]"
);
}
}
// length of major axis
if (Type.isNumber(parents[2])) {
majorAxis = Type.createFunction(parents[2], board);
} else if (Type.isFunction(parents[2]) && Type.isNumber(parents[2]())) {
majorAxis = parents[2];
} else {
// point on ellipse
if (Type.isPoint(parents[2])) {
C = board.select(parents[2]);
// point on ellipse given by coordinates
} else if (parents[2].length > 1) {
C = board.create("point", parents[2], attr_foci);
// given by function
} else if (Type.isFunction(parents[2]) && Type.isPoint(parents[2]())) {
C = parents[2]();
// focus i given by point name
} else if (Type.isString(parents[2])) {
C = board.select(parents[2]);
} else {
throw new Error(
"JSXGraph: Can't create Hyperbola with parent types '" +
typeof parents[0] +
"' and '" +
typeof parents[1] +
"' and '" +
typeof parents[2] +
"'." +
"\nPossible parent types: [point,point,point], [point,point,number|function]"
);
}
/** @ignore */
majorAxis = function () {
return C.Dist(F[0]) - C.Dist(F[1]);
};
}
// to
if (!Type.exists(parents[4])) {
parents[4] = 1.0001 * Math.PI;
}
// from
if (!Type.exists(parents[3])) {
parents[3] = -1.0001 * Math.PI;
}
M = board.create(
"point",
[
function () {
return (F[0].X() + F[1].X()) * 0.5;
},
function () {
return (F[0].Y() + F[1].Y()) * 0.5;
}
],
attr_center
);
/**
* @class
* @ignore
*/
curve = board.create(
"curve",
[
function (x) {
return 0;
},
function (x) {
return 0;
},
parents[3],
parents[4]
],
attr_curve
);
curve.majorAxis = majorAxis;
// Hyperbola is defined by (a*sec(t),b*tan(t)) and sec(t) = 1/cos(t)
/** @ignore */
polarForm = function (phi, suspendUpdate) {
var r, rr, ax, ay, bx, by, axbx, ayby, f;
if (!suspendUpdate) {
r = majorAxis();
rr = r * r;
ax = F[0].X();
ay = F[0].Y();
bx = F[1].X();
by = F[1].Y();
axbx = ax - bx;
ayby = ay - by;
f = (rr - ax * ax - ay * ay + bx * bx + by * by) / (2 * r);
curve.quadraticform = [
[f * f - bx * bx - by * by, (f * axbx) / r + bx, (f * ayby) / r + by],
[(f * axbx) / r + bx, (axbx * axbx) / rr - 1, (axbx * ayby) / rr],
[(f * ayby) / r + by, (axbx * ayby) / rr, (ayby * ayby) / rr - 1]
];
}
};
/** @ignore */
curve.X = function (phi, suspendUpdate) {
var r = majorAxis(),
c = F[1].Dist(F[0]),
b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) + r),
beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());
if (!suspendUpdate) {
polarForm(phi, suspendUpdate);
}
return F[0].X() + Math.cos(beta + phi) * b;
};
/** @ignore */
curve.Y = function (phi, suspendUpdate) {
var r = majorAxis(),
c = F[1].Dist(F[0]),
b = (0.5 * (c * c - r * r)) / (c * Math.cos(phi) + r),
beta = Math.atan2(F[1].Y() - F[0].Y(), F[1].X() - F[0].X());
return F[0].Y() + Math.sin(beta + phi) * b;
};
curve.midpoint = curve.center = M;
curve.subs = {
center: curve.center
};
curve.inherits.push(curve.center, F[0], F[1]);
if (Type.isPoint(C)) {
curve.inherits.push(C);
}
curve.type = Const.OBJECT_TYPE_CONIC;
M.addChild(curve);
for (i = 0; i < 2; i++) {
if (Type.isPoint(F[i])) {
F[i].addChild(curve);
}
}
if (Type.isPoint(C)) {
C.addChild(curve);
}
curve.setParents(parents);
return curve;
};
/**
* @class A parabola is a special conic section given by one point (the focus) and a line (the directrix).
*
* @pseudo
* @name Parabola
* @elementclass curve
* @augments JXG.Curve
* @constructor
* @type JXG.Curve
* @see Conic
* @see Ellipse
* @see Hyperbola
* @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
*/
/**
* @jsxgraphsignature Parabola
* Parent elements are a point and a line or a pair of coordinates.
* Optional parameters three and four are numbers which define the curve length (e.g. start/end).
* Default values are -π and π.
* @param {PointLike} point
* @param {Line} line
* @param {Number} [start=-π] parameter of the curve start, default: -π.
* @param {Number} [end=π] parameter for the curve end, default: π.
*
* @example <caption>Create a parabola by a point C and a line l</caption>
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var l = board.create('line', [A,B]);
* var C = board.create('point', [1,1]);
* var el = board.create('parabola',[C,l]);
* </pre><div class="jxgbox" id="JXG524d1aae-217d-44d4-ac58-a19c7ab1de36" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function() {
* var board = JXG.JSXGraph.initBoard('JXG524d1aae-217d-44d4-ac58-a19c7ab1de36', {boundingbox:[-6,6,6,-6], keepaspectratio:true, showcopyright: false, shownavigation: false});
* var A = board.create('point', [-1,4]);
* var B = board.create('point', [-1,-4]);
* var l = board.create('line', [A,B]);
* var C = board.create('point', [1,1]);
* var el = board.create('parabola',[C,l]);
* })();
* </script><pre>
*
* @example <caption>Create a parabola by a point and a line, both given by coordinate pairs</caption>
* var par = board.create('parabola',[[3.25, 0], [[0.25, 1],[0.25, 0]]]);
*
* </pre><div id="JXG09252542-b77a-4990-a109-66ffb649a472" class="jxgbox" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function() {
* var board = JXG.JSXGraph.initBoard('JXG09252542-b77a-4990-a109-66ffb649a472',
* {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
* var par = board.create('parabola',[[3.25, 0], [[0.25, 1],[0.25, 0]]]);
*
* })();
*
* </script><pre>
*
*/
JXG.createParabola = function (board, parents, attributes) {
var polarForm,
curve,
M,
// focus
F1 = parents[0],
// directrix
l = parents[1],
attr_foci = Type.copyAttributes(attributes, board.options, "conic", 'foci'),
attr_center = Type.copyAttributes(attributes, board.options, "conic", 'center'),
attr_curve = Type.copyAttributes(attributes, board.options, 'conic'),
attr_line;
// focus 1 given by coordinates
if (parents[0].length > 1) {
F1 = board.create("point", parents[0], attr_foci);
// focus 1 given by point
} else if (Type.isPoint(parents[0])) {
F1 = board.select(parents[0]);
// given by function
} else if (Type.isFunction(parents[0]) && Type.isPoint(parents[0]())) {
F1 = parents[0]();
// focus 1 given by point name
} else if (Type.isString(parents[0])) {
F1 = board.select(parents[0]);
} else {
throw new Error(
"JSXGraph: Can't create Parabola with parent types '" +
typeof parents[0] +
"' and '" +
typeof parents[1] +
"'." +
"\nPossible parent types: [point,line]"
);
}
// Create line if given as array of two points.
if (Type.isArray(l) && l.length === 2) {
attr_line = Type.copyAttributes(attributes, board.options, "conic", 'line');
l = board.create("line", l, attr_line);
}
// to
if (!Type.exists(parents[3])) {
parents[3] = 2 * Math.PI;
}
// from
if (!Type.exists(parents[2])) {
parents[2] = 0;
}
M = board.create(
"point",
[
function () {
/*
var v = [0, l.stdform[1], l.stdform[2]];
v = Mat.crossProduct(v, F1.coords.usrCoords);
return Geometry.meetLineLine(v, l.stdform, 0, board).usrCoords;
*/
return Geometry.projectPointToLine(F1, l, board).usrCoords;
}
],
attr_center
);
/**
* @class
* @ignore
*/
curve = board.create(
"curve",
[
function (x) {
return 0;
},
function (x) {
return 0;
},
parents[2],
parents[3]
],
attr_curve
);
curve.midpoint = curve.center = M;
curve.subs = {
center: curve.center
};
curve.inherits.push(curve.center);
/** @ignore */
polarForm = function (t, suspendUpdate) {
var a, b, c, ab, px, py;
if (!suspendUpdate) {
a = l.stdform[1];
b = l.stdform[2];
c = l.stdform[0];
ab = a * a + b * b;
px = F1.X();
py = F1.Y();
curve.quadraticform = [
[c * c - ab * (px * px + py * py), c * a + ab * px, c * b + ab * py],
[c * a + ab * px, -b * b, a * b],
[c * b + ab * py, a * b, -a * a]
];
}
};
/** @ignore */
curve.X = function (phi, suspendUpdate) {
var a,
det,
beta = l.getAngle(),
d = Geometry.distPointLine(F1.coords.usrCoords, l.stdform),
A = l.point1.coords.usrCoords,
B = l.point2.coords.usrCoords,
M = F1.coords.usrCoords;
// Handle the case if one of the two defining points of the line is an ideal point
if (A[0] === 0) {
A = [1, B[1] + l.stdform[2], B[2] - l.stdform[1]];
} else if (B[0] === 0) {
B = [1, A[1] + l.stdform[2], A[2] - l.stdform[1]];
}
det = (B[1] - A[1]) * (M[2] - A[2]) - (B[2] - A[2]) * (M[1] - A[1]) >= 0 ? 1 : -1;
a = (det * d) / (1 - Math.sin(phi));
if (!suspendUpdate) {
polarForm(phi, suspendUpdate);
}
return F1.X() + Math.cos(phi + beta) * a;
};
/** @ignore */
curve.Y = function (phi, suspendUpdate) {
var a,
det,
beta = l.getAngle(),
d = Geometry.distPointLine(F1.coords.usrCoords, l.stdform),
A = l.point1.coords.usrCoords,
B = l.point2.coords.usrCoords,
M = F1.coords.usrCoords;
// Handle the case if one of the two defining points of the line is an ideal point
if (A[0] === 0) {
A = [1, B[1] + l.stdform[2], B[2] - l.stdform[1]];
} else if (B[0] === 0) {
B = [1, A[1] + l.stdform[2], A[2] - l.stdform[1]];
}
det = (B[1] - A[1]) * (M[2] - A[2]) - (B[2] - A[2]) * (M[1] - A[1]) >= 0 ? 1 : -1;
a = (det * d) / (1 - Math.sin(phi));
return F1.Y() + Math.sin(phi + beta) * a;
};
curve.type = Const.OBJECT_TYPE_CONIC;
M.addChild(curve);
if (Type.isPoint(F1)) {
F1.addChild(curve);
curve.inherits.push(F1);
}
l.addChild(curve);
curve.setParents(parents);
return curve;
};
/**
*
* @class Create a generic conic section either by five points or the coefficients of the general conic's equation.
* If the conic section is defined by the coefficients of the equation
* \\[Ax^2+ Bxy+Cy^2 + Dx + Ey + F = 0\\]
* then the parameters are as follows:
* ```
* board.create('conic', [A, C, F, B/2, D/2, E/2]);
* ```
* @pseudo
* @name Conic
* @elementclass curve
* @augments JXG.Curve
* @constructor
* @type JXG.Curve
* @see Ellipse
* @see Hyperbola
* @see Parabola
* @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
*/
/**
* @jsxgraphsignature Conic
* Parent elements are five points.
* @param {PointLike} A
* @param {PointLike} B
* @param {PointLike} C
* @param {PointLike} D
* @param {PointLike} E
* @example <caption>Create a conic section through the points A, B, C, D, and E</caption>
* var A = board.create('point', [1,5]);
* var B = board.create('point', [1,2]);
* var C = board.create('point', [2,0]);
* var D = board.create('point', [0,0]);
* var E = board.create('point', [-1,5]);
* var conic = board.create('conic',[A,B,C,D,E]);
* </pre><div class="jxgbox" id="JXG2d79bd6a-db9b-423c-9cba-2497f0b06320" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function(){
* var board = JXG.JSXGraph.initBoard('JXG2d79bd6a-db9b-423c-9cba-2497f0b06320', {boundingbox:[-6,6,6,-6], keepaspectratio:true, showcopyright: false, shownavigation: false});
* var A = board.create('point', [1,5]);
* var B = board.create('point', [1,2]);
* var C = board.create('point', [2,0]);
* var D = board.create('point', [0,0]);
* var E = board.create('point', [-1,5]);
* var conic = board.create('conic',[A,B,C,D,E]);
* })();
* </script><pre>
*/
/**
* @jsxgraphsignature Conic
* Parent elements are 6 numbers, i.e. A, C, F, B/2, D/2, E/2
* @param {NumberLike} a_00
* @param {NumberLike} a_11
* @param {NumberLike} a_22
* @param {NumberLike} a_01
* @param {NumberLike} a_02
* @param {NumberLike} a_12
*
* @example <caption>Conic given by numbers A, C, F, B/2, D/2, E/2</caption>
* var conic = board.create('conic', [1, 2, -4, 0, 0, 0]);
*
* </pre><div id="JXG8576a04a-52d8-4a7e-8d54-e32443910b97" class="jxgbox" style="width: 300px; height: 300px;"></div>
* <script type="text/javascript">
* (function() {
* var board = JXG.JSXGraph.initBoard('JXG8576a04a-52d8-4a7e-8d54-e32443910b97',
* {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
* // Parameters: A, C, F, B/2, D/2, E/2
* var conic = board.create('conic', [1, 2, -4, 0, 0, 0]);
* })();
*
* </script><pre>
*
*/
JXG.createConic = function (board, parents, attributes) {
var polarForm,
curve,
fitConic,
degconic,
sym,
eigen,
a,
b,
c,
c1,
c2,
i,
definingMat,
givenByPoints,
rotationMatrix = [
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]
],
M = [
[1, 0, 0],
[0, 1, 0],
[0, 0, 1]
],
points = [],
p = [],
attr_point = Type.copyAttributes(attributes, board.options, "conic", 'point'),
attr_center = Type.copyAttributes(attributes, board.options, "conic", 'center'),
attr_curve = Type.copyAttributes(attributes, board.options, 'conic');
if (parents.length === 5) {
givenByPoints = true;
} else if (parents.length === 6) {
givenByPoints = false;
} else {
throw new Error(
"JSXGraph: Can't create generic Conic with " + parents.length + " parameters."
);
}
if (givenByPoints) {
for (i = 0; i < 5; i++) {
// point i given by coordinates
if (parents[i].length > 1) {
points[i] = board.create("point", parents[i], attr_point);
// point i given by point
} else if (Type.isPoint(parents[i])) {
points[i] = board.select(parents[i]);
// given by function
} else if (Type.isFunction(parents[i]) && Type.isPoint(parents[i]())) {
points[i] = parents[i]();
// point i given by point name
} else if (Type.isString(parents[i])) {
points[i] = board.select(parents[i]);
} else {
throw new Error(
"JSXGraph: Can't create Conic section with parent types '" +
typeof parents[i] +
"'." +
"\nPossible parent types: [point,point,point,point,point], [a00,a11,a22,a01,a02,a12]"
);
}
}
} else {
/* Usual notation (x,y,z):
* [[A0,A3,A4],
* [A3,A1,A5],
* [A4,A5,A2]].
* Our notation (z,x,y):
* [[A2, A4, A5],
* [A4, A0, A3],
* [A5, A3, A1]]
*/
definingMat = [
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
];
definingMat[0][0] = Type.isFunction(parents[2])
? function () {
return parents[2]();
}
: function () {
return parents[2];
};
definingMat[0][1] = Type.isFunction(parents[4])
? function () {
return parents[4]();
}
: function () {
return parents[4];
};
definingMat[0][2] = Type.isFunction(parents[5])
? function () {
return parents[5]();
}
: function () {
return parents[5];
};
definingMat[1][1] = Type.isFunction(parents[0])
? function () {
return parents[0]();
}
: function () {
return parents[0];
};
definingMat[1][2] = Type.isFunction(parents[3])
? function () {
return parents[3]();
}
: function () {
return parents[3];
};
definingMat[2][2] = Type.isFunction(parents[1])
? function () {
return parents[1]();
}
: function () {
return parents[1];
};
}
// sym(A) = A + A^t . Manipulates A in place.
sym = function (A) {
var i, j;
for (i = 0; i < 3; i++) {
for (j = i; j < 3; j++) {
A[i][j] += A[j][i];
}
}
for (i = 0; i < 3; i++) {
for (j = 0; j < i; j++) {
A[i][j] = A[j][i];
}
}
return A;
};
// degconic(v,w) = sym(v*w^t)
degconic = function (v, w) {
var i,
j,
mat = [
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
];
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
mat[i][j] = v[i] * w[j];
}
}
return sym(mat);
};
// (p^t*B*p)*A-(p^t*A*p)*B
fitConic = function (A, B, p) {
var i,
j,
pBp,
pAp,
Mv,
mat = [
[0, 0, 0],
[0, 0, 0],
[0, 0, 0]
];
Mv = Mat.matVecMult(B, p);
pBp = Mat.innerProduct(p, Mv);
Mv = Mat.matVecMult(A, p);
pAp = Mat.innerProduct(p, Mv);
for (i = 0; i < 3; i++) {
for (j = 0; j < 3; j++) {
mat[i][j] = pBp * A[i][j] - pAp * B[i][j];
}
}
return mat;
};
// Here, the defining functions for the curve are just dummy functions.
// In polarForm there is a reference to curve.quadraticform.
/**
* @class
* @ignore
*/
curve = board.create(
"curve",
[
function (x) {
return 0;
},
function (x) {
return 0;
},
0,
2 * Math.PI
],
attr_curve
);
/** @ignore */
polarForm = function (phi, suspendUpdate) {
var i, j, v; // len,;
if (!suspendUpdate) {
if (givenByPoints) {
// Copy the point coordinate vectors
for (i = 0; i < 5; i++) {
p[i] = points[i].coords.usrCoords;
}
// Compute the quadratic form
c1 = degconic(Mat.crossProduct(p[0], p[1]), Mat.crossProduct(p[2], p[3]));
c2 = degconic(Mat.crossProduct(p[0], p[2]), Mat.crossProduct(p[1], p[3]));
M = fitConic(c1, c2, p[4]);
} else {
for (i = 0; i < 3; i++) {
for (j = i; j < 3; j++) {
M[i][j] = definingMat[i][j]();
if (j > i) {
M[j][i] = M[i][j];
}
}
}
}
// Here is the reference back to the curve.
curve.quadraticform = M;
// Compute Eigenvalues and Eigenvectors
eigen = Numerics.Jacobi(M);
// Scale the Eigenvalues such that the first Eigenvalue is positive
if (eigen[0][0][0] < 0) {
eigen[0][0][0] *= -1;
eigen[0][1][1] *= -1;
eigen[0][2][2] *= -1;
}
// Normalize the Eigenvectors
// for (i = 0; i < 3; i++) {
// // len = Mat.hypot(eigen[1][0][i], eigen[1][1][i], eigen[1][2][i])
// for (j = 0; j < 3; j++) {
// len += eigen[1][j][i] * eigen[1][j][i];
// }
// len = Math.sqrt(len);
// /*for (j = 0; j < 3; j++) {
// //eigen[1][j][i] /= len;
// }*/
// }
rotationMatrix = eigen[1];
c = Math.sqrt(Math.abs(eigen[0][0][0]));
a = Math.sqrt(Math.abs(eigen[0][1][1]));
b = Math.sqrt(Math.abs(eigen[0][2][2]));
}
// The degenerate cases with eigen[0][i][i]==0 are not handled correct yet.
if (eigen[0][1][1] <= 0.0 && eigen[0][2][2] <= 0.0) {
v = Mat.matVecMult(rotationMatrix, [1 / c, Math.cos(phi) / a, Math.sin(phi) / b]);
} else if (eigen[0][1][1] <= 0.0 && eigen[0][2][2] > 0.0) {
v = Mat.matVecMult(rotationMatrix, [Math.cos(phi) / c, 1 / a, Math.sin(phi) / b]);
} else if (eigen[0][2][2] < 0.0) {
v = Mat.matVecMult(rotationMatrix, [Math.sin(phi) / c, Math.cos(phi) / a, 1 / b]);
}
if (Type.exists(v)) {
// Normalize
v[1] /= v[0];
v[2] /= v[0];
v[0] = 1.0;
} else {
v = [1, NaN, NaN];
}
return v;
};
/** @ignore */
curve.X = function (phi, suspendUpdate) {
return polarForm(phi, suspendUpdate)[1];
};
/** @ignore */
curve.Y = function (phi, suspendUpdate) {
return polarForm(phi, suspendUpdate)[2];
};
// Center coordinates see https://en.wikipedia.org/wiki/Matrix_representation_of_conic_sections
curve.midpoint = board.create(
"point",
[
function () {
var m = curve.quadraticform;
return [
m[1][1] * m[2][2] - m[1][2] * m[1][2],
m[1][2] * m[0][2] - m[2][2] * m[0][1],
m[0][1] * m[1][2] - m[1][1] * m[0][2]
];
}
],
attr_center
);
curve.type = Const.OBJECT_TYPE_CONIC;
curve.center = curve.midpoint;
curve.subs = {
center: curve.center
};
curve.inherits.push(curve.center);
curve.inherits = curve.inherits.concat(points);
if (givenByPoints) {
for (i = 0; i < 5; i++) {
if (Type.isPoint(points[i])) {
points[i].addChild(curve);
}
}
curve.setParents(parents);
}
curve.addChild(curve.center);
return curve;
};
JXG.registerElement("ellipse", JXG.createEllipse);
JXG.registerElement("hyperbola", JXG.createHyperbola);
JXG.registerElement("parabola", JXG.createParabola);
JXG.registerElement("conic", JXG.createConic);
// export default {
// createEllipse: JXG.createEllipse,
// createHyperbola: JXG.createHyperbola,
// createParabola: JXG.createParabola,
// createConic: JXG.createConic
// };