Design for Create Track
This page explains the design behind the 'createTrack' function which you use to build tracks that provide data for a carriage to follow. A track is built for an array of points (Vector3s) which is split into sections. Each section uses the designated lean, the rotation of the carriage about the track direction and turn, the rotation of the carriage about its local Y axis, of the carriage following the track to produce arrays of matrices for each point on the track path. The direction of a rail is given by the tilt (-π/2 to π/2) of the rail about the z axis and its swivel ( to to 2π) about the y axis.
Rotation Matrices
Matrices are used since they are the fundamental operations needed to combine rotations in a given order. To produce the final rotation of a carriage at any point all the following rotations: tilt; swivel; lean; turn; need to be combined.
Obtaining the Track Data
The track data produce by createTrack
are the arrays
- directions: directions of travel;
- rotations: a combination of the lean and turn rotations;
- carriageRotations: lean rotations;
- passengerRotations: turn rotations.
The parameters needed for each section are
- start index;
then the options
- lean;
- leanTwists;
- leanWaves;
- leanWaveAngle;
- turn;
- turnTwists;
- turnWaves;
- turnWaveAngle.
are used with
var section = new sectionData(startAt, options)
The code for which is
var sectionData = function (startAt, options) {this.start = startAt;this.options = options;}
This data for each section is passed as an array to 'createTrack' along with the points for the track as
var createTrack = function(points, sections) {
Internally 'createTrack' uses a 'createSection' function to construct the data to return.
Section Build
The 'createSection' takes three parameters, points, the full points array for the track, the startSection which contains the information to be used in creating the section and endSection which just provides the lean and turn values at the end of the current section.
The term rail is used to indicate a segment of track from points[i] to points[i + 1]
function createSection(points, startSection, endSection) {/***** Calculate the number of rails for the section *****/var railsFrom = startSection.start; //index of start of sectionvar railsTo = endSection.start; //index of end of sectionif(endSection.start === 0) {railsTo = points.length;}var nbRails = railsTo - railsFrom;/***** Set the defaults for the section *****/var initialLean = (startSection.options.lean === void 0) ? 0 : startSection.options.lean; //lean of carriage about direction axis at start, a phi variablevar initialTurn = (startSection.options.turn === void 0) ? 0 : startSection.options.turn; // turn of carriage around upright at start, a theta variablevar leanTwists = (startSection.options.leanTwists === void 0) ? 0 : startSection.options.leanTwists; //number of lean twists (+ve counter clockwise, -ve clockwise)var leanWaves = (startSection.options.leanWaves === void 0) ? 0 : startSection.options.leanWaves; //number of lean wavesvar leanWaveAngle = (startSection.options.leanWaveAngle === void 0) ? 0 : startSection.options.leanWaveAngle; //angle for lean wavevar turnTwists = (startSection.options.turnTwists === void 0) ? 0 : startSection.options.turnTwists; //number of turn twists (+ve counter clockwise, -ve clockwise)var turnWaves = (startSection.options.turnWaves === void 0) ? 0 : startSection.options.turnWaves; //number of turn wavesvar turnWaveAngle = (startSection.options.turnWaveAngle === void 0) ? 0 : startSection.options.turnWaveAngle; //angle for turn wavevar finalLean = (endSection.options.lean === void 0) ? 0 : endSection.options.lean;var finalTurn = (endSection.options.turn === void 0) ? 0 : endSection.options.turn;/***** Check if both waves and twists are used and ignore twists when so *****///lean waves supersede lean twists unless leanWaveAngle = 0if (leanWaves > 0 && Math.abs(leanTwists) > 0) {if (leanWaveAngle == 0) {leanWaves = 0;}else {leanTwists = 0;}}//turn waves supersede turn twists unless turnWaveAngle = 0if (turnWaves > 0 && Math.abs(turnTwists) > 0) {if (turnWaveAngle == 0) {turnWaves = 0;}else {turnTwists = 0;}}/***** Initiate the variables and their types *****///rail transformation matrices for swivel and tilt rotationsvar rotationMatrixY = BABYLON.Matrix.Identity();var rotationMatrixZ = BABYLON.Matrix.Identity();var rotationMatrix = BABYLON.Matrix.Identity();var m = BABYLON.Matrix.Identity();var initialRailDirection = BABYLON.Axis.X;var initialUprightDirection = BABYLON.Axis.Y;var initialLevelDirection = BABYLON.Axis.Z;var railDirection = BABYLON.Vector3.Zero();var uprightDirection = BABYLON.Vector3.Zero(); //contains vector normal to rail direction after tiltvar levelDirection = BABYLON.Vector3.Zero(); //contains vector normal to rail direction after swivelvar leanDirection = BABYLON.Vector3.Zero(); // contains vector normal to rail direction after tilt, swivel and leanvar turnDirection = BABYLON.Vector3.Zero();var carriageNormal = BABYLON.Vector3.Zero();var rotationMatrixLean = BABYLON.Matrix.Identity();var rotationMatrixTurn = BABYLON.Matrix.Identity();var rotationMatrixPassenger = BABYLON.Matrix.Identity();var initialPosition = BABYLON.Vector3.Zero();var rotation = BABYLON.Matrix.Identity(); //Overall rotation after tilt, swivel, lean and turnvar tilt = 0; //tilt angle of rail after rotation about (0, 0, 1)var swivel = 0 //swivel angle of rail after rotation around (0, 1, 0)var railCount = 0; // determines how many rails along a section, used to control wave values//Set calculated values for variablesvar phi = initialLean;var theta = initialTurn;var gradLean = (finalLean - initialLean) / (nbRails - 1); // lean gradientvar gradTurn = (finalTurn - initialTurn) / (nbRails - 1); // turn gradientvar deltaPhi = (finalLean + 2 * leanTwists * Math.PI - initialLean) / (nbRails); //increase in phi per rail for lean twistvar deltaTheta = (finalTurn + 2 * turnTwists * Math.PI - initialTurn) / (nbRails); //increase in theta per rail for lean twist/***** Loop over rails in section*****/for (var i = railsFrom; i < railsTo; i++) {points[(i + 1) % points.length].subtractToRef(points[i], railDirection); //direction of each railrailDirection.normalize();swivel = -Math.atan2(railDirection.z, railDirection.x); //swivel angle rail makes in xz planetilt = Math.atan2(Math.abs(railDirection.y), Math.abs(railDirection.x)); // tilt angle rail makes in first quadrant of xy planetilt *= Math.sign(railDirection.y); //tilt angle of rail in xy plane from -pi/2 to pi/2BABYLON.Matrix.RotationAxisToRef(BABYLON.Axis.Y, swivel, rotationMatrixY); //swivel angle to matrix rotationBABYLON.Matrix.RotationAxisToRef(BABYLON.Axis.Z, tilt, rotationMatrixZ); //tilt angle to matrix rotationrotationMatrixZ.multiplyToRef(rotationMatrixY, rotationMatrix); // form combined swivel and tilt matrixBABYLON.Vector3.TransformNormalToRef(initialUprightDirection, rotationMatrix, uprightDirection); //swivel, tilt act on carriage uprightBABYLON.Vector3.TransformNormalToRef(initialLevelDirection, rotationMatrix, levelDirection); //swivel, tilt act on carriage leveluprightDirection.normalize();levelDirection.normalize();if (leanWaves > 0) {phi = initialLean + railCount * gradLean + leanWaveAngle * Math.sin(railCount * leanWaves * Math.PI / (nbRails - 1));}else {phi += deltaPhi;}if (turnWaves > 0) {theta = initialTurn + railCount * gradTurn + turnWaveAngle * Math.sin(railCount * turnWaves * Math.PI / (nbRails - 1));}else {theta += deltaTheta;}railCount++;BABYLON.Matrix.RotationAxisToRef(railDirection, phi, rotationMatrixLean); // lean matrixBABYLON.Vector3.TransformNormalToRef(uprightDirection, rotationMatrixLean, carriageNormal); // lean applied to uprightBABYLON.Matrix.RotationAxisToRef(carriageNormal, theta, rotationMatrixTurn); // turn applied to upright after leanBABYLON.Matrix.RotationAxisToRef(initialUprightDirection, theta, rotationMatrixPassenger); //just turn applied to uprightpassengerRotations.push(rotationMatrixPassenger.clone());rotationMatrix.multiplyToRef(rotationMatrixLean, rotation); //rotation from swivel, tilt, and lean onlycarriageRotations.push(rotation.clone());rotation.multiplyToRef(rotationMatrixTurn, rotation); //complete rotation from swivel, tilt, lean and turnrotations.push(rotation.clone())directions.push(railDirection.clone());}}
Create Track from Sections
The createTrack function requires the points for the path of the track and an array of sections. Checking is carried out on the order of sections.
var createTrack = function(points, sections) {//Data arraysvar directions = [];var rotations = [];var carriageRotations = [];var passengerRotations = [];var nbSections = sections.length;var looped = (sections[nbSections - 1].start === 0);for(var i = 1; i < nbSections - looped; i++) {if (sections[i - 1].start > sections[i].start) {console.log("sections not in order");return;}}if (0 < sections[nbSections - 1].start && sections[nbSections - 2].start > sections[nbSections - 1].start) {console.log("last section not in order");return;}var section = sections[0];if (section.start > 0) {startSection = new sectionData(0, {});sections.unshift(startSection);nbSections = sections.length;}if (0 < sections[nbSections - 1].start && sections[nbSections - 1].start < points.length - 1) { //assume need to close loopvar endSection = new sectionData(0, sections[0].options);sections.push(endSection);}//Store track data per sectionfor (var i = 0; i < sections.length - 1; i++) {createSection(points, sections[i], sections[i + 1]);}return {directions: directions, rotations:rotations, carriageRotations: carriageRotations, passengerRotations: passengerRotations}/****** createSection function goes here *******/}