Vector class - Node.js Data Structure

Description

Vector class

Demo Code

/*//  w w w.j  a v  a 2s  . c  om
 * Copyright (C) 2007 Apple Inc.  All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE COMPUTER, INC. ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE COMPUTER, INC. OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
 */

function createVector(x,y,z) {
    return new Array(x,y,z);
}

function sqrLengthVector(self) {
    return self[0] * self[0] + self[1] * self[1] + self[2] * self[2];
}

function lengthVector(self) {
    return Math.sqrt(self[0] * self[0] + self[1] * self[1] + self[2] * self[2]);
}

function addVector(self, v) {
    self[0] += v[0];
    self[1] += v[1];
    self[2] += v[2];
    return self;
}

function subVector(self, v) {
    self[0] -= v[0];
    self[1] -= v[1];
    self[2] -= v[2];
    return self;
}

function scaleVector(self, scale) {
    self[0] *= scale;
    self[1] *= scale;
    self[2] *= scale;
    return self;
}

function normaliseVector(self) {
    var len = Math.sqrt(self[0] * self[0] + self[1] * self[1] + self[2] * self[2]);
    self[0] /= len;
    self[1] /= len;
    self[2] /= len;
    return self;
}

function add(v1, v2) {
    return new Array(v1[0] + v2[0], v1[1] + v2[1], v1[2] + v2[2]);
}

function sub(v1, v2) {
    return new Array(v1[0] - v2[0], v1[1] - v2[1], v1[2] - v2[2]);
}

function scalev(v1, v2) {
    return new Array(v1[0] * v2[0], v1[1] * v2[1], v1[2] * v2[2]);
}

function dot(v1, v2) {
    return v1[0] * v2[0] + v1[1] * v2[1] + v1[2] * v2[2];
}

function scale(v, scale) {
    return [v[0] * scale, v[1] * scale, v[2] * scale];
}

function cross(v1, v2) {
    return [v1[1] * v2[2] - v1[2] * v2[1], 
            v1[2] * v2[0] - v1[0] * v2[2],
            v1[0] * v2[1] - v1[1] * v2[0]];

}

function normalise(v) {
    var len = lengthVector(v);
    return [v[0] / len, v[1] / len, v[2] / len];
}

function transformMatrix(self, v) {
    var vals = self;
    var x  = vals[0] * v[0] + vals[1] * v[1] + vals[2] * v[2] + vals[3];
    var y  = vals[4] * v[0] + vals[5] * v[1] + vals[6] * v[2] + vals[7];
    var z  = vals[8] * v[0] + vals[9] * v[1] + vals[10] * v[2] + vals[11];
    return [x, y, z];
}

function invertMatrix(self) {
    var temp = new Array(16);
    var tx = -self[3];
    var ty = -self[7];
    var tz = -self[11];
    for (h = 0; h < 3; h++) 
        for (v = 0; v < 3; v++) 
            temp[h + v * 4] = self[v + h * 4];
    for (i = 0; i < 11; i++)
        self[i] = temp[i];
    self[3] = tx * self[0] + ty * self[1] + tz * self[2];
    self[7] = tx * self[4] + ty * self[5] + tz * self[6];
    self[11] = tx * self[8] + ty * self[9] + tz * self[10];
    return self;
}


// Triangle intersection using barycentric coord method
function Triangle(p1, p2, p3) {
    var edge1 = sub(p3, p1);
    var edge2 = sub(p2, p1);
    var normal = cross(edge1, edge2);
    if (Math.abs(normal[0]) > Math.abs(normal[1]))
        if (Math.abs(normal[0]) > Math.abs(normal[2]))
            this.axis = 0; 
        else 
            this.axis = 2;
    else
        if (Math.abs(normal[1]) > Math.abs(normal[2])) 
            this.axis = 1;
        else 
            this.axis = 2;
    var u = (this.axis + 1) % 3;
    var v = (this.axis + 2) % 3;
    var u1 = edge1[u];
    var v1 = edge1[v];
    
    var u2 = edge2[u];
    var v2 = edge2[v];
    this.normal = normalise(normal);
    this.nu = normal[u] / normal[this.axis];
    this.nv = normal[v] / normal[this.axis];
    this.nd = dot(normal, p1) / normal[this.axis];
    var det = u1 * v2 - v1 * u2;
    this.eu = p1[u];
    this.ev = p1[v]; 
    this.nu1 = u1 / det;
    this.nv1 = -v1 / det;
    this.nu2 = v2 / det;
    this.nv2 = -u2 / det; 
    this.material = [0.7, 0.7, 0.7];
}

Triangle.prototype.intersect = function(orig, dir, near, far) {
    var u = (this.axis + 1) % 3;
    var v = (this.axis + 2) % 3;
    var d = dir[this.axis] + this.nu * dir[u] + this.nv * dir[v];
    var t = (this.nd - orig[this.axis] - this.nu * orig[u] - this.nv * orig[v]) / d;
    if (t < near || t > far)
        return null;
    var Pu = orig[u] + t * dir[u] - this.eu;
    var Pv = orig[v] + t * dir[v] - this.ev;
    var a2 = Pv * this.nu1 + Pu * this.nv1;
    if (a2 < 0) 
        return null;
    var a3 = Pu * this.nu2 + Pv * this.nv2;
    if (a3 < 0) 
        return null;

    if ((a2 + a3) > 1) 
        return null;
    return t;
}

function Scene(a_triangles) {
    this.triangles = a_triangles;
    this.lights = [];
    this.ambient = [0,0,0];
    this.background = [0.8,0.8,1];
}
var zero = new Array(0,0,0);

Scene.prototype.intersect = function(origin, dir, near, far) {
    var closest = null;
    for (i = 0; i < this.triangles.length; i++) {
        var triangle = this.triangles[i];   
        var d = triangle.intersect(origin, dir, near, far);
        if (d == null || d > far || d < near)
            continue;
        far = d;
        closest = triangle;
    }
    
    if (!closest)
        return [this.background[0],this.background[1],this.background[2]];
        
    var normal = closest.normal;
    var hit = add(origin, scale(dir, far)); 
    if (dot(dir, normal) > 0)
        normal = [-normal[0], -normal[1], -normal[2]];
    
    var colour = null;
    if (closest.shader) {
        colour = closest.shader(closest, hit, dir);
    } else {
        colour = closest.material;
    }
    
    // do reflection
    var reflected = null;
    if (colour.reflection > 0.001) {
        var reflection = addVector(scale(normal, -2*dot(dir, normal)), dir);
        reflected = this.intersect(hit, reflection, 0.0001, 1000000);
        if (colour.reflection >= 0.999999)
            return reflected;
    }
    
    var l = [this.ambient[0], this.ambient[1], this.ambient[2]];
    for (var i = 0; i < this.lights.length; i++) {
        var light = this.lights[i];
        var toLight = sub(light, hit);
        var distance = lengthVector(toLight);
        scaleVector(toLight, 1.0/distance);
        distance -= 0.0001;
        if (this.blocked(hit, toLight, distance))
            continue;
        var nl = dot(normal, toLight);
        if (nl > 0)
            addVector(l, scale(light.colour, nl));
    }
    l = scalev(l, colour);
    if (reflected) {
        l = addVector(scaleVector(l, 1 - colour.reflection), scaleVector(reflected, colour.reflection));
    }
    return l;
}

Scene.prototype.blocked = function(O, D, far) {
    var near = 0.0001;
    var closest = null;
    for (i = 0; i < this.triangles.length; i++) {
        var triangle = this.triangles[i];   
        var d = triangle.intersect(O, D, near, far);
        if (d == null || d > far || d < near)
            continue;
        return true;
    }
    
    return false;
}

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