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index.js
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index.js
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//#---------- file: "log.js"
/*
Function that prints log messages.
Copyright 2013 Guillaume Lathoud
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
A copy of the Apache License Version 2.0 as of February 20th, 2013
can be found in the file ./LICENSE.TXT
*/
(function (G) {
if (G.log)
return;
G.log = log;
function log(s)
{
if (typeof console !== 'undefined')
console.log(s); // Browsers
else
print(s); // V8, Rhino
}
})(this);
//#---------- end of file: "log.js"
//#---------- file: "complex.js"
/*
Functions to create and manipulate complex numbers.
Copyright 2013 Guillaume Lathoud
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
A copy of the Apache License Version 2.0 as of February 20th, 2013
can be found in the file ./LICENSE.TXT
*/
(function (/*global*/G) {
if (G.Complex)
return;
var epsilon = 1e-5;
// Public API
G.cplx = cplx;
G.Complex = Complex;
G.cadd = cadd;
G.csub = csub;
G.cmul = cmul;
G.cdiv = cdiv;
G.cpol = cpol;
G.croot = croot;
// Implementation
function cadd(a,b) { return cplx(a).add( cplx(b) ); }
function csub(a,b) { return cplx(a).sub( cplx(b) ); }
function cmul(a,b) { return cplx(a).mul( cplx(b) ); }
function cdiv(a,b) { return cplx(a).div( cplx(b) ); }
function croot(a, n, /*?optional 0<k<=n?*/k) { return cplx(a).root(n, k); }
function cplx(a,b) { return a instanceof Complex ? a : new Complex(a, b); }
function cpol(r,angle) { return new Complex(r*Math.cos(angle),r*Math.sin(angle)); }
function Complex(re,im)
{
this.re = re || 0;
this.im = im || 0;
}
var Cp = Complex.prototype;
Cp.toString = Cp.toValue = function () {
throw new Error('Complex does not support toString / toValue - to ease debugging');
};
Cp.str = function () {
var re = this.re
, im = this.im
;
return this.ltEps() ? '<ltEps: ' + re.toPrecision(4) + '+i*' + im.toPrecision(4) + '>' : re + '+i*' + im;
};
Cp.add = function (other) {
return cplx(this.re+other.re,this.im+other.im);
};
Cp.sub = function (other) {
return cplx(this.re-other.re,this.im-other.im);
};
Cp.mul = function (other) {
return cplx(this.re*other.re-this.im*other.im,
this.re*other.im+this.im*other.re
);
};
Cp.div = function (other) {
return this.mul(other.conj()).mul( cplx( 1 / other.r2() ) );
};
Cp.conj = function () {
return cplx(this.re, -this.im);
}
Cp.root = function (/*integer*/n, /*?integer?*/k) {
// Just return *one* of the roots
k != null || (k = 0); // Default value
if (typeof n !== 'number' || n !== ~~n)
throw new Error('complex root: n must be an integer. You gave: ' + n);
if (typeof k !== 'number' || k !== ~~k)
throw new Error('complex root: k must be an integer. You gave: ' + k);
var r = Math.pow(this.r2(), 1/(2*n))
, angle = Math.atan2(this.im,this.re) / n
;
return cpol(r,angle + k * 2 * Math.PI / n );
}
Cp.r2 = function () {
return this.re*this.re+this.im*this.im;
}
Cp.ltEps = function () {
return this.r2() < epsilon*epsilon;
}
Cp.isReal = function () {
return this.ltEps() || ( this.im * this.im / this.r2() ) < epsilon * epsilon;
}
})(this);
//#---------- end of file: "complex.js"
//#---------- file: "solve_quartic.js"
/*
ECMAScript implementation of the algebraic resolution of quartic
equations, based on the Renaissance works of Ferrari and Vieta.
Copyright 2013 Guillaume Lathoud
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
A copy of the Apache License Version 2.0 as of February 20th, 2013
can be found in the file ./LICENSE.TXT
*/
/*global load Quartic cadd cmul cdiv csub croot log cplx*/
if (typeof load !== 'undefined')
{
load('log.js');
load('complex.js');
}
var quartic;
(function (G) {
if (quartic)
return;
// API
quartic = {
getRootsQuartic : getRootsQuartic
, getRootsCubic : getRootsCubic
, getRootsDepressedCubic : getRootsDepressedCubic
, getRootsQuadratic : getRootsQuadratic
};
// API Implementation
function getRootsQuartic( /*number | Complex*/A, B, C, D, E, /*?boolean?*/verbose )
// Find the roots of a quartic polynomial
//
// f(x) = A x^4 + B x^3 + C x^2 + D x + E
//
// that is the four values x1, x2, x3, x4
// verifying f(x) = 0
//
// The implementation
// below is general (complexes all the way).
//
// It uses Ferrari's approach:
// http://en.wikipedia.org/wiki/Quartic_function
//
// including Vieta's substitution for the depressed cubic:
// http://en.wikipedia.org/wiki/Cubic_equation#Vieta.27s_substitution
//
// Guillaume Lathoud
// 2012-12-17
{
// First, convert to a depressed quartic:
//
// x = u - B / 4A
//
// u^4 + alpha * u^2 + beta * u + gamma = 0
var A2 = cmul( A, A )
, A3 = cmul( A, A2 )
, A4 = cmul( A, A3 )
, B2 = cmul( B, B )
, B3 = cmul( B, B2 )
, B4 = cmul( B, B3 )
, alpha = cmul( -3, B2 ).div( cmul( 8, A2) ).add( C.div( A ) )
, beta = B3.div( cmul( 8, A3 ) ).sub( B.mul(C).div( cmul( 2, A2 ))).add(D.div(A))
, gamma = cmul( -3, B4 ).div( cmul( 256, A4 ) ).add( C.mul(B2).div( cmul(16,A3))).sub(B.mul(D).div(cmul(4,A2))).add(E.div(A))
;
if (verbose)
{
log('');
log('depressed quartic:');
log('alpha ' + alpha.str());
log('beta ' + beta.str());
log('gamma ' + gamma.str());
}
var u1,u2,u3,u4; // Where the `u` roots values will be stored
if (beta.ltEps())
quartic_solve_biquadratic();
else if (gamma.ltEps())
quartic_solve_depressed_cubic();
else
quartic_solve_non_degenerate_quartic();
var bdfa = B.div( cmul( 4, A ));
if (verbose)
{
log('');
log('B/4A: ' + bdfa.str());
}
var x1 = u1.sub(bdfa)
, x2 = u2.sub(bdfa)
, x3 = u3.sub(bdfa)
, x4 = u4.sub(bdfa)
;
return [ x1, x2, x3, x4 ];
function quartic_solve_depressed_cubic()
// u4 = 0 is a root.
//
// For the 3 other roots:
//
// u^3 + alpha*u + beta = 0 the depressed cubic equation
{
if (verbose)
{
log('');
log('quartic_solve_depressed_cubic');
}
var uroots = getRootsDepressedCubic( 1, alpha, beta, verbose );
u1 = uroots[ 0 ];
u2 = uroots[ 1 ];
u3 = uroots[ 2 ];
u4 = cplx( 0 );
}
function quartic_solve_biquadratic()
// (u^2)^2 + alpha * (u^2) + gamma = 0
{
if (verbose)
{
log('');
log('quartic_solve_biquadratic');
}
var qroots = getRootsQuadratic( 1, alpha, gamma, verbose )
, u2_1 = qroots[ 0 ]
, u2_2 = qroots[ 1 ]
;
u1 = biquadratic_solution( u2_1, -1 );
u2 = biquadratic_solution( u2_1, +1 );
u3 = biquadratic_solution( u2_2, -1 );
u4 = biquadratic_solution( u2_2, +1 );
}
function biquadratic_solution( u2, sign )
{
return cmul( sign > 0 ? +1: -1 , croot( u2, 2 ) );
}
function quartic_solve_non_degenerate_quartic()
{
// nested depressed cubic:
var alpha2 = alpha.mul(alpha)
, alpha3 = alpha.mul(alpha2)
, P = cdiv( alpha2, -12 ).sub( gamma )
, Q = cdiv( alpha3, -108 ).add( cdiv( alpha.mul(gamma), 3 )).sub( cdiv( beta.mul(beta), 8 ) )
, tmp = croot( cdiv( Q.mul(Q), 4 ).add( cdiv( P.mul(P).mul(P), 27 ))
, 2
)
, R1 = cadd( cdiv( Q, -2 ), tmp)
// R2 = csub( cdiv( Q, -2 ), tmp); // R1 enough
, U = croot(R1, 3)
, V = U.ltEps() ? croot(Q,3) : cdiv( cdiv(P,3),U)
, y = cmul( -5/6, alpha ).add(U).sub( V )
;
if (verbose)
{
log('');
log('nested depressed cubic:');
log('P ' + P.str());
log('Q ' + Q.str());
log('U ' + U.str());
log('V ' + V.str());
log('y ' + y.str());
}
// Folding the second perfect square
var W = croot(cadd(alpha,cmul(2,y)), 2)
, taty = cadd( cmul(3,alpha) , cmul(2, y) )
, tbw = cdiv( cmul(2,beta) , W )
;
if (verbose)
{
log('');
log('Folding the second perfect square');
log('W ' + W.str());
}
u1 = Wbtt_2_u( W, bdfa, taty, tbw, -1, -1 );
u2 = Wbtt_2_u( W, bdfa, taty, tbw, -1, +1 );
u3 = Wbtt_2_u( W, bdfa, taty, tbw, +1, -1 );
u4 = Wbtt_2_u( W, bdfa, taty, tbw, +1, +1 );
function Wbtt_2_u( W, bdfa, taty, tbw, s, t )
{
return cmul
( 0.5
, cadd
( cmul( s, W )
, cmul
( t
, croot
( cmul
( -1
, cadd( taty, cmul( s, tbw ) )
)
, 2
)
)
)
);
}
}
} // end of: getRootsQuartic
function getRootsCubic( A, B, C, D, verbose )
// Find the three roots of the cubic equation:
//
// A * x^3 + B * x^2 + C * x + D = 0
//
// Let: x = u - B / 3A
//
// Then:
//
// A * u^3 + P * u + Q = 0
//
// http://en.wikipedia.org/wiki/Cubic_equation#Reduction_to_a_depressed_cubic
{
var A2 = cmul( A, A )
, B2 = cmul( B, B )
, B3 = B2.mul( B )
, P = csub( C, B2.div( cmul( 3, A ) ) )
, Q = cmul( 2, B3 )
.sub( cmul( 9, cmul( A, cmul( B, C ) ) ) )
.add( cmul( 27, cmul( A2, D ) ) )
.div( cmul( 27, A2 ) )
, dcroots = getRootsDepressedCubic( A, P, Q, verbose )
, u1 = dcroots[ 0 ]
, u2 = dcroots[ 1 ]
, u3 = dcroots[ 2 ]
, bdta = cdiv( B, cmul( 3, A ) )
, x1 = u1.sub( bdta )
, x2 = u2.sub( bdta )
, x3 = u3.sub( bdta )
;
if (verbose)
{
log('');
log('bdta: ' + bdta.str());
}
return [ x1, x2, x3 ];
}
function getRootsDepressedCubic( A, C, D, verbose )
// Find the three roots of the depressed cubic equation:
//
// A * x^3 + C * x + D = 0
//
// Let:
// alpha = C / A
// beta = D / A
//
// then:
// x^3 + alpha * x + beta = 0
//
// The Vieta's substitution [vieta]:
//
// x = w - alpha / 3w
//
// results in the equation:
//
// w^3 + beta - alpha^3 / (27 * w^3) = 0
//
// (w^3)^2 + beta (w^3) - alpha^3 / 27 = 0
//
// -> solve the quadratic to find one value of w^3
// -> compute the 3 roots w1 w2 w3 and thus x1 x2 x3
//
// [vieta] http://en.wikipedia.org/wiki/Cubic_equation#Vieta.27s_substitution
{
var alpha = cdiv( C, A )
, beta = cdiv( D, A )
, delta = quadratic_delta( 1
, beta
, cdiv( alpha.mul(alpha).mul(alpha), -27)
)
, wcube = quadratic_root(1, beta, delta, +1)
, w1 = wcube.root(3,0)
, w2 = wcube.root(3,1)
, w3 = wcube.root(3,2)
, x1 = w2u( w1 )
, x2 = w2u( w2 )
, x3 = w2u( w3 )
;
if (verbose)
{
log('');
log('wcube ' + wcube.str());
log('w1 ' + w1.str() + ' ' + (w1.mul(w1).mul(w1).sub(wcube)).ltEps());
log('w2 ' + w2.str() + ' ' + (w2.mul(w2).mul(w2).sub(wcube)).ltEps())
log('w3 ' + w3.str() + ' ' + (w3.mul(w3).mul(w3).sub(wcube)).ltEps());
}
return [x1, x2, x3];
function w2u( w )
{
return w.sub( alpha.div( cmul(3,w) ) );
}
}
function getRootsQuadratic( A, B, C, verbose )
// A * x^2 + B * x + C = 0
{
var delta = quadratic_delta( A, B, C )
, x1 = quadratic_root( A, B, delta, +1 )
, x2 = quadratic_root( A, B, delta, -1 )
;
if (verbose)
{
log('');
log('delta: ' + delta.str() );
log('x1: ' + x1.str() );
log('x2: ' + x2.str() );
}
return [ x1, x2 ];
}
// ----------------------------------------------------------------------
// Private details
function quadratic_delta(a,b,c)
{
return cmul( b, b ).sub( cmul( 4, cmul( a, c ) ) )
}
function quadratic_root( a,b,delta,sign )
// a*x^2 + b*x + c = 0
// delta = b^2-4*a*c
{
return cdiv(
cmul(-1, b)[ sign > 0 ? 'add' : 'sub']( croot( delta, 2 ))
, cmul(2, a)
);
}
})();
//#---------- end of file: "solve_quartic.js"
//#---------- file: "solve_problem.js"
/*
Solution to the specific ramp problem described in ./index.html
Required files: ./quartic.js ./complex.js ./log.js
Copyright 2013 Guillaume Lathoud
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
A copy of the Apache License Version 2.0 as of February 20th, 2013
can be found in the file ./LICENSE.TXT
*/
/*global quartic try_to_solve*/
function try_to_solve( /*object*/problem )
{
var horizlength = problem.horizlength
, width = problem.width
, qq = problem.qq
;
// Make sure we have all numbers
horizlength.toPrecision.call.a , width.toPrecision.call.a , qq.toPrecision.call.a;
/*
Problem, viewed from above, projected onto the horizontal plane:
|<---qq-->|
| steep slope
| (60deg) | i*zz + horizlength * exp(i*angle)
| |
i*zz | rampe
| | rampe
| rampe_(slope not steep)_(xx+i*qq)__________
| ^
| yy*exp(i*angle) steep slope (60deg) qq
o________________________________________________v
Goal: Build a *rectangular* rampe of not-steep-slope 25% to go down
some depth. The above graph represents the "steep slope" and the four
points of the rampe, projected in the horizontal plane.
Projected onto the horizontal complex plane, the rampe is a rectangle
`horizlength*with` with the four edge points:
i*zz
yy*exp(i*angle)
xx+i*qq
i*zz + horizlength * exp(i*angle)
Assumptions/goals: the three points o (origin), yy*exp(i*angle) and
xx+i*qq must be aligned. Also, i*zz coincides with the top of the
steep slope and xx+i*qq coincides with the bottom of the steep slope.
Note that horizlength must be > qq so that the
slope of the rampe is less than the slope of 60deg.
One can show that qq*width=xx*yy (look e.g. at tan(angle))
and that:
f(yy)=0
where f(yy):=yy^2*((horizlength+yy)^2-qq^2)-qq*qq*width*width
The problem was given to me initially by Felix Schaedler.
I solve f(yy)=0 first quickly, using dichotomy (see ./OLD/).
Below, a direct solution that implements Ferrari's approach to find
the 4 roots of any quartic equation (complex or real coefficients - in
our application we have real coefficients).
Ferrari's approach: http://en.wikipedia.org/wiki/Quartic_function
The implementation below is general (complexes all the way).
Guillaume Lathoud
2012-11-28
Numerical results:
application-specific: look for a positive real root
yy_solution 0.49281701552540547
f(yy_solution) 0+i*0
f(yy_solution).ltEps() true
angle_solution_radians 0.13988524363241306
angle_solution_degrees 8.014834076296541
xx_solution 14.35125122462075
xx_solution-qq 12.33052528245706
zz_solution 3.5345252313134456
*/
// Use case values A B C D E are fed into the generic complex
// implementation, which finds the four roots x1 x2 x3 x4 of the
// quartic equation f(yy)=0
// The problem described above (rampe)
// Application-specific values (reals)
//
// This leads to a non-degenerate quartic.
A = cplx( 1 );
B = cplx( 2 * horizlength );
C = cplx( horizlength*horizlength - qq*qq );
D = cplx( 0 );
E = cplx( -qq*qq*width*width );
function f(yy)
{
yy = cplx(yy);
var yy2 = yy.mul(yy)
, yy3 = yy.mul(yy2)
, yy4 = yy.mul(yy3)
;
return cmul( A, yy4 ).add( cmul( B, yy3 ) ).add( cmul( C, yy2 ) ).add( cmul( D, yy ) ).add( E );
}
// Solve: find four roots
var roots = quartic.getRootsQuartic( A, B, C, D, E, /*verbose:*/true )
, x1 = roots[ 0 ]
, x2 = roots[ 1 ]
, x3 = roots[ 2 ]
, x4 = roots[ 3 ]
;
// Check that these really are roots of f(yy)
var fx1 = f(x1), fx2 = f(x2), fx3 = f(x3), fx4 = f(x4)
, verif1 = fx1.ltEps()
, verif2 = fx2.ltEps()
, verif3 = fx3.ltEps()
, verif4 = fx4.ltEps()
;
log('');
log('roots:');
log('x1 ' + x1.str() + ' -> f(x1) ' + fx1.str() + ' verif1:' + verif1);
log('x2 ' + x2.str() + ' -> f(x2) ' + fx2.str() + ' verif2:' + verif2);
log('x3 ' + x3.str() + ' -> f(x3) ' + fx3.str() + ' verif3:' + verif3);
log('x4 ' + x4.str() + ' -> f(x4) ' + fx4.str() + ' verif4:' + verif4);
if (!(verif1*verif2*verif3*verif4))
throw new Error('At least one of x1,x2,x3,x4 is not a root!');
log('');
log('--> ROOTS OK!');
log('');
// Application-specific: try to look for a positive real root
var yy_solution = null
, candidates = [ x1, x2, x3, x4 ]
;
for (var i = candidates.length; i--;)
{
var c = candidates[i];
if (!c.isReal())
continue;
yy_solution = Math.max( yy_solution || -Infinity, c.re );
}
log('');
log('application-specific: try to look for a positive real root');
log('yy_solution ' + yy_solution);
var solution = null;
if (yy_solution == null)
log('-> not found.');
else
{
log('-> found.');
log('');
log('f(yy_solution) ' + f(yy_solution).str());
var verification = f(yy_solution).ltEps();
log('f(yy_solution).ltEps() ' + verification);
if(!verification)
throw new Error('Something is wrong!');
log('');
// Application-specific: derive other values
angle_solution_radians = Math.atan2(yy_solution,width);
angle_solution_degrees = angle_solution_radians / Math.PI * 180;
xx_solution = qq*width/yy_solution;
zz_solution = Math.sqrt(width*width+yy_solution*yy_solution);
log('angle_solution_radians ' + angle_solution_radians);
log('angle_solution_degrees ' + angle_solution_degrees);
log('xx_solution ' + xx_solution);
log('xx_solution-qq ' + (xx_solution-qq));
log('zz_solution ' + zz_solution);
solution = {
xx : xx_solution
, yy : yy_solution
, zz : zz_solution
, angle_radians : angle_solution_radians
, angle_degrees : angle_solution_degrees
};
}
log('');
return solution;
}
//#---------- end of file: "solve_problem.js"
//#---------- file: "trackballcontrols.js"
/**
* @author Eberhard Graether / http://egraether.com/
*/
THREE.TrackballControls = function ( object, domElement ) {
THREE.EventDispatcher.call( this );
var _this = this;
var STATE = { NONE: -1, ROTATE: 0, ZOOM: 1, PAN: 2, TOUCH_ROTATE: 3, TOUCH_ZOOM: 4, TOUCH_PAN: 5 };
this.object = object;
this.domElement = ( domElement !== undefined ) ? domElement : document;
// API
this.enabled = true;
this.screen = { width: 0, height: 0, offsetLeft: 0, offsetTop: 0 };
this.radius = ( this.screen.width + this.screen.height ) / 4;
this.rotateSpeed = 1.0;
this.zoomSpeed = 1.2;
this.panSpeed = 0.3;
this.noRotate = false;
this.noZoom = false;
this.noPan = false;
this.staticMoving = false;
this.dynamicDampingFactor = 0.2;
this.minDistance = 0;
this.maxDistance = Infinity;
this.keys = [ 65 /*A*/, 83 /*S*/, 68 /*D*/ ];
// internals
this.target = new THREE.Vector3();
var lastPosition = new THREE.Vector3();
var _state = STATE.NONE,
_prevState = STATE.NONE,
_eye = new THREE.Vector3(),
_rotateStart = new THREE.Vector3(),
_rotateEnd = new THREE.Vector3(),
_zoomStart = new THREE.Vector2(),
_zoomEnd = new THREE.Vector2(),
_touchZoomDistanceStart = 0,
_touchZoomDistanceEnd = 0,
_panStart = new THREE.Vector2(),
_panEnd = new THREE.Vector2();
// events
var changeEvent = { type: 'change' };
// methods
this.handleResize = function () {
this.screen.width = window.innerWidth;
this.screen.height = window.innerHeight;
this.screen.offsetLeft = 0;
this.screen.offsetTop = 0;
this.radius = ( this.screen.width + this.screen.height ) / 4;
};
this.handleEvent = function ( event ) {
if ( typeof this[ event.type ] == 'function' ) {
this[ event.type ]( event );
}
};
this.getMouseOnScreen = function ( clientX, clientY ) {
return new THREE.Vector2(
( clientX - _this.screen.offsetLeft ) / _this.radius * 0.5,
( clientY - _this.screen.offsetTop ) / _this.radius * 0.5
);
};
this.getMouseProjectionOnBall = function ( clientX, clientY ) {
var mouseOnBall = new THREE.Vector3(
( clientX - _this.screen.width * 0.5 - _this.screen.offsetLeft ) / _this.radius,
( _this.screen.height * 0.5 + _this.screen.offsetTop - clientY ) / _this.radius,
0.0
);
var length = mouseOnBall.length();
if ( length > 1.0 ) {
mouseOnBall.normalize();
} else {
mouseOnBall.z = Math.sqrt( 1.0 - length * length );
}
_eye.copy( _this.object.position ).sub( _this.target );
var projection = _this.object.up.clone().setLength( mouseOnBall.y );
projection.add( _this.object.up.clone().cross( _eye ).setLength( mouseOnBall.x ) );
projection.add( _eye.setLength( mouseOnBall.z ) );
return projection;
};
this.rotateCamera = function () {
var angle = Math.acos( _rotateStart.dot( _rotateEnd ) / _rotateStart.length() / _rotateEnd.length() );
if ( angle ) {
var axis = ( new THREE.Vector3() ).crossVectors( _rotateStart, _rotateEnd ).normalize(),
quaternion = new THREE.Quaternion();
angle *= _this.rotateSpeed;
quaternion.setFromAxisAngle( axis, -angle );
_eye.applyQuaternion( quaternion );
_this.object.up.applyQuaternion( quaternion );
_rotateEnd.applyQuaternion( quaternion );
if ( _this.staticMoving ) {
_rotateStart.copy( _rotateEnd );
} else {
quaternion.setFromAxisAngle( axis, angle * ( _this.dynamicDampingFactor - 1.0 ) );
_rotateStart.applyQuaternion( quaternion );
}
}
};
this.zoomCamera = function () {
if ( _state === STATE.TOUCH_ZOOM ) {
var factor = _touchZoomDistanceStart / _touchZoomDistanceEnd;
_touchZoomDistanceStart = _touchZoomDistanceEnd;
_eye.multiplyScalar( factor );
} else {
var factor = 1.0 + ( _zoomEnd.y - _zoomStart.y ) * _this.zoomSpeed;
if ( factor !== 1.0 && factor > 0.0 ) {
_eye.multiplyScalar( factor );
if ( _this.staticMoving ) {
_zoomStart.copy( _zoomEnd );
} else {
_zoomStart.y += ( _zoomEnd.y - _zoomStart.y ) * this.dynamicDampingFactor;
}
}
}
};
this.panCamera = function () {
var mouseChange = _panEnd.clone().sub( _panStart );
if ( mouseChange.lengthSq() ) {
mouseChange.multiplyScalar( _eye.length() * _this.panSpeed );
var pan = _eye.clone().cross( _this.object.up ).setLength( mouseChange.x );
pan.add( _this.object.up.clone().setLength( mouseChange.y ) );
_this.object.position.add( pan );
_this.target.add( pan );
if ( _this.staticMoving ) {
_panStart = _panEnd;
} else {
_panStart.add( mouseChange.subVectors( _panEnd, _panStart ).multiplyScalar( _this.dynamicDampingFactor ) );
}
}
};
this.checkDistances = function () {
if ( !_this.noZoom || !_this.noPan ) {
if ( _this.object.position.lengthSq() > _this.maxDistance * _this.maxDistance ) {
_this.object.position.setLength( _this.maxDistance );