three.js/test/unit/src/extras/curves/CatmullRomCurve3.js

/**
 * @author zz85 / http://joshuakoo.com
 */

QUnit.module( "CatmullRomCurve3" );

var positions = [
	new THREE.Vector3( - 60, - 100,  60 ),
	new THREE.Vector3( - 60,   20,  60 ),
	new THREE.Vector3( - 60,  120,  60 ),
	new THREE.Vector3(  60,   20, - 60 ),
	new THREE.Vector3(  60, - 100, - 60 )
];

QUnit.test( "catmullrom check", function( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var expectedPoints = [

		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 60, - 51.04, 60 ),
		new THREE.Vector3( - 60, - 2.7199999999999998, 60 ),
		new THREE.Vector3( - 61.92, 44.48, 61.92 ),
		new THREE.Vector3( - 68.64, 95.36000000000001, 68.64 ),
		new THREE.Vector3( - 60, 120, 60 ),
		new THREE.Vector3( - 14.880000000000017, 95.36000000000001, 14.880000000000017 ),
		new THREE.Vector3( 41.75999999999997, 44.48000000000003, - 41.75999999999997 ),
		new THREE.Vector3( 67.68, - 2.720000000000023, - 67.68 ),
		new THREE.Vector3( 65.75999999999999, - 51.04000000000001, - 65.75999999999999 ),
		new THREE.Vector3( 60, - 100, - 60 )

	];

	var points = curve.getPoints( 10 );

	assert.equal( points.length, expectedPoints.length, 'correct number of points.' );

	points.forEach( function ( point, i ) {

		assert.numEqual( point.x, expectedPoints[ i ].x, 'points[' + i + '].x' );
		assert.numEqual( point.y, expectedPoints[ i ].y, 'points[' + i + '].y' );
		assert.numEqual( point.z, expectedPoints[ i ].z, 'points[' + i + '].z' );

	} );

} );

QUnit.test( "chordal basic check", function( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );

	curve.type = 'chordal';

	var expectedPoints = [
		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 60, - 52, 60 ),
		new THREE.Vector3( - 60, - 4, 60 ),
		new THREE.Vector3( - 60.656435889910924, 41.62455386421379, 60.656435889910924 ),
		new THREE.Vector3( - 62.95396150459915, 87.31049238896205, 62.95396150459915 ),
		new THREE.Vector3( - 60, 120, 60 ),
		new THREE.Vector3( - 16.302568199486444, 114.1500463116312, 16.302568199486444 ),
		new THREE.Vector3( 42.998098664956586, 54.017050116427455, - 42.998098664956586 ),
		new THREE.Vector3( 63.542500175682434, - 1.137153397546383, - 63.542500175682434 ),
		new THREE.Vector3( 62.65687513176183, - 49.85286504815978, - 62.65687513176183 ),
		new THREE.Vector3( 60.00000000000001, - 100, - 60.00000000000001 )
	];

	var points = curve.getPoints( 10 );

	assert.equal( points.length, expectedPoints.length, 'correct number of points.' );

	points.forEach( function ( point, i ) {

		assert.numEqual( point.x, expectedPoints[ i ].x, 'points[' + i + '].x' );
		assert.numEqual( point.y, expectedPoints[ i ].y, 'points[' + i + '].y' );
		assert.numEqual( point.z, expectedPoints[ i ].z, 'points[' + i + '].z' );

	} );

} );

QUnit.test( "centripetal basic check", function( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'centripetal';

	var expectedPoints = [
		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 60, - 51.47527724919028, 60 ),
		new THREE.Vector3( - 60, - 3.300369665587032, 60 ),
		new THREE.Vector3( - 61.13836565863938, 42.86306307781241, 61.13836565863938 ),
		new THREE.Vector3( - 65.1226454638772, 90.69743905511538, 65.1226454638772 ),
		new THREE.Vector3( - 60, 120, 60 ),
		new THREE.Vector3( - 15.620412575504497, 103.10790870179872, 15.620412575504497 ),
		new THREE.Vector3( 42.384384731047874, 48.35477686933143, - 42.384384731047874 ),
		new THREE.Vector3( 65.25545512241153, - 1.646250966068339, - 65.25545512241153 ),
		new THREE.Vector3( 63.94159134180865, - 50.234688224551256, - 63.94159134180865 ),
		new THREE.Vector3( 59.99999999999999, - 100, - 59.99999999999999 ),
	];

	var points = curve.getPoints( 10 );

	assert.equal( points.length, expectedPoints.length, 'correct number of points.' );

	points.forEach( function ( point, i ) {

		assert.numEqual( point.x, expectedPoints[ i ].x, 'points[' + i + '].x' );
		assert.numEqual( point.y, expectedPoints[ i ].y, 'points[' + i + '].y' );
		assert.numEqual( point.z, expectedPoints[ i ].z, 'points[' + i + '].z' );

	} );

} );

QUnit.test( "closed catmullrom basic check", function( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';
	curve.closed = true;

	var expectedPoints = [
		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 67.5, - 46.25, 67.5 ),
		new THREE.Vector3( - 60, 20, 60 ),
		new THREE.Vector3( - 67.5, 83.75, 67.5 ),
		new THREE.Vector3( - 60, 120, 60 ),
		new THREE.Vector3( 0, 83.75, 0 ),
		new THREE.Vector3( 60, 20, - 60 ),
		new THREE.Vector3( 75, - 46.25, - 75 ),
		new THREE.Vector3( 60, - 100, - 60 ),
		new THREE.Vector3( 0, - 115, 0 ),
		new THREE.Vector3( - 60, - 100, 60 ),
	];

	var points = curve.getPoints( 10 );

	assert.equal( points.length, expectedPoints.length, 'correct number of points.' );

	points.forEach( function ( point, i ) {

		assert.numEqual( point.x, expectedPoints[ i ].x, 'points[' + i + '].x' );
		assert.numEqual( point.y, expectedPoints[ i ].y, 'points[' + i + '].y' );
		assert.numEqual( point.z, expectedPoints[ i ].z, 'points[' + i + '].z' );

	} );

} );


//
// curve.type = 'catmullrom'; only from here on
//
QUnit.test( "getLength/getLengths", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var length = curve.getLength();
	var expectedLength = 551.549686276872;

	assert.numEqual( length, expectedLength, "Correct length of curve" );

	var expectedLengths = [
		0,
		120,
		220,
		416.9771560359221,
		536.9771560359221
	];
	var lengths = curve.getLengths( expectedLengths.length - 1 );

	assert.strictEqual( lengths.length, expectedLengths.length, "Correct number of segments" );

	lengths.forEach( function ( segment, i ) {

		assert.numEqual( segment, expectedLengths[ i ], "segment[" + i + "] correct" );

	} );

} );

QUnit.test( "getPointAt", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var expectedPoints = [
		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 64.84177333183106, 64.86956465359813, 64.84177333183106 ),
		new THREE.Vector3( - 28.288507045700854, 104.83101184518996, 28.288507045700854 ),
		new THREE.Vector3( 60, - 100, - 60 )
	];

	var points = [
		curve.getPointAt( 0 ),
		curve.getPointAt( 0.3 ),
		curve.getPointAt( 0.5 ),
		curve.getPointAt( 1 )
	];

	assert.deepEqual( points, expectedPoints, "Correct points" );

} );

QUnit.test( "getTangent/getTangentAt", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var expectedTangents = [
		new THREE.Vector3( 0, 1, 0 ),
		new THREE.Vector3( - 0.0001090274561657922, 0.9999999881130137, 0.0001090274561657922 ),
		new THREE.Vector3( 0.7071067811865475, - 2.0930381713877622e-13, - 0.7071067811865475 ),
		new THREE.Vector3( 0.43189437062802816, - 0.7917919583070032, - 0.43189437062802816 ),
		new THREE.Vector3( - 0.00019991333100812723, - 0.9999999600346592, 0.00019991333100812723 )
	];

	var tangents = [
		curve.getTangent( 0 ),
		curve.getTangent( 0.25 ),
		curve.getTangent( 0.5 ),
		curve.getTangent( 0.75 ),
		curve.getTangent( 1 )
	];

	expectedTangents.forEach( function ( exp, i ) {

		var tangent = tangents[ i ];

		assert.numEqual( tangent.x, exp.x, "getTangent #" + i + ": x correct" );
		assert.numEqual( tangent.y, exp.y, "getTangent #" + i + ": y correct" );

	} );

	//

	expectedTangents = [
		new THREE.Vector3( 0, 1, 0 ),
		new THREE.Vector3( - 0.10709018822205997, 0.9884651653817284, 0.10709018822205997 ),
		new THREE.Vector3( 0.6396363672964268, - 0.4262987629159402, - 0.6396363672964268 ),
		new THREE.Vector3( 0.5077298411616501, - 0.6960034603275557, - 0.5077298411616501 ),
		new THREE.Vector3( - 0.00019991333100812723, - 0.9999999600346592, 0.00019991333100812723 )
	];

	tangents = [
		curve.getTangentAt( 0 ),
		curve.getTangentAt( 0.25 ),
		curve.getTangentAt( 0.5 ),
		curve.getTangentAt( 0.75 ),
		curve.getTangentAt( 1 )
	];

	expectedTangents.forEach( function ( exp, i ) {

		var tangent = tangents[ i ];

		assert.numEqual( tangent.x, exp.x, "getTangentAt #" + i + ": x correct" );
		assert.numEqual( tangent.y, exp.y, "getTangentAt #" + i + ": y correct" );

	} );

} );

QUnit.test( "computeFrenetFrames", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var expected = {
		binormals: [
			new THREE.Vector3( - 1, 0, 0 ),
			new THREE.Vector3( - 0.28685061854203, 0.6396363672964267, - 0.7131493814579701 ),
			new THREE.Vector3( - 1.9982670528160395e-8, - 0.0001999133310081272, - 0.9999999800173295 )
		],
		normals: [
			new THREE.Vector3( 0, 0, - 1 ),
			new THREE.Vector3( - 0.7131493814579699, - 0.6396363672964268, - 0.2868506185420297 ),
			new THREE.Vector3( - 0.9999999800173294, 0.00019991333100810582, - 1.99826701852146e-8 )
		],
		tangents: [
			new THREE.Vector3( 0, 1, 0 ),
			new THREE.Vector3( 0.6396363672964269, - 0.4262987629159403, - 0.6396363672964269 ),
			new THREE.Vector3( - 0.0001999133310081273, - 0.9999999600346594, 0.0001999133310081273 )
		]
	};

	var frames = curve.computeFrenetFrames( 2, false );

	Object.keys( expected ).forEach( function ( group, i ) {

		expected[ group ].forEach( function ( vec, j ) {

			assert.numEqual( frames[ group ][ j ].x, vec.x, "Frenet frames [" + i + ", " + j + "].x correct" );
			assert.numEqual( frames[ group ][ j ].y, vec.y, "Frenet frames [" + i + ", " + j + "].y correct" );
			assert.numEqual( frames[ group ][ j ].z, vec.z, "Frenet frames [" + i + ", " + j + "].z correct" );

		} );

	} );

} );

QUnit.test( "getUtoTmapping", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var start = curve.getUtoTmapping( 0, 0 );
	var end = curve.getUtoTmapping( 0, curve.getLength() );
	var somewhere = curve.getUtoTmapping( 0.5, 500 );

	var expectedSomewhere = 0.8964116382083199;

	assert.strictEqual( start, 0, "getUtoTmapping( 0, 0 ) is the starting point" );
	assert.strictEqual( end, 1, "getUtoTmapping( 0, length ) is the ending point" );
	assert.numEqual( somewhere, expectedSomewhere, "getUtoTmapping( 0.5, 500 ) is correct" );

} );

QUnit.test( "getSpacedPoints", function ( assert ) {

	var curve = new THREE.CatmullRomCurve3( positions );
	curve.type = 'catmullrom';

	var expectedPoints = [
		new THREE.Vector3( - 60, - 100, 60 ),
		new THREE.Vector3( - 60, 10.311489426555056, 60 ),
		new THREE.Vector3( - 65.05889864636504, 117.99691802595966, 65.05889864636504 ),
		new THREE.Vector3( 6.054276900088592, 78.7153118386369, - 6.054276900088592 ),
		new THREE.Vector3( 64.9991491385602, 8.386980812799566, - 64.9991491385602 ),
		new THREE.Vector3( 60, - 100, - 60 )
	];

	var points = curve.getSpacedPoints();

	assert.strictEqual( points.length, expectedPoints.length, "Correct number of points" );
	assert.deepEqual( points, expectedPoints, "Correct points calculated" );

} );