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@@ -3723,23 +3723,24 @@ class Quaternion {
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random() {
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- // Derived from http://planning.cs.uiuc.edu/node198.html
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- // Note, this source uses w, x, y, z ordering,
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- // so we swap the order below.
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+ // sets this quaternion to a uniform random unit quaternnion
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- const u1 = Math.random();
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- const sqrt1u1 = Math.sqrt( 1 - u1 );
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- const sqrtu1 = Math.sqrt( u1 );
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+ // Ken Shoemake
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+ // Uniform random rotations
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+ // D. Kirk, editor, Graphics Gems III, pages 124-132. Academic Press, New York, 1992.
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- const u2 = 2 * Math.PI * Math.random();
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+ const theta1 = 2 * Math.PI * Math.random();
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+ const theta2 = 2 * Math.PI * Math.random();
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- const u3 = 2 * Math.PI * Math.random();
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+ const x0 = Math.random();
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+ const r1 = Math.sqrt( 1 - x0 );
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+ const r2 = Math.sqrt( x0 );
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return this.set(
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- sqrt1u1 * Math.cos( u2 ),
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- sqrtu1 * Math.sin( u3 ),
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- sqrtu1 * Math.cos( u3 ),
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- sqrt1u1 * Math.sin( u2 ),
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+ r1 * Math.sin( theta1 ),
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+ r1 * Math.cos( theta1 ),
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+ r2 * Math.sin( theta2 ),
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+ r2 * Math.cos( theta2 ),
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);
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}
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@@ -4507,15 +4508,15 @@ class Vector3 {
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randomDirection() {
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- // Derived from https://mathworld.wolfram.com/SpherePointPicking.html
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+ // https://mathworld.wolfram.com/SpherePointPicking.html
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- const u = ( Math.random() - 0.5 ) * 2;
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- const t = Math.random() * Math.PI * 2;
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- const f = Math.sqrt( 1 - u ** 2 );
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+ const theta = Math.random() * Math.PI * 2;
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+ const u = Math.random() * 2 - 1;
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+ const c = Math.sqrt( 1 - u * u );
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- this.x = f * Math.cos( t );
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- this.y = f * Math.sin( t );
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- this.z = u;
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+ this.x = c * Math.cos( theta );
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+ this.y = u;
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+ this.z = c * Math.sin( theta );
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return this;
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Mugen87