359 lines
14 KiB
JavaScript
359 lines
14 KiB
JavaScript
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(function(window){
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// A Javascript 2D vector library
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// conventions :
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// method that returns a float value do not modify the vector
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// method that implement operators return a new vector with the modifications without
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// modifying the calling vector or the parameters.
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//
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// v3 = v1.add(v2); // v3 is set to v1 + v2, v1, v2 are not modified
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//
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// methods that take a single vector as a parameter are usually also available with
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// q '_xy' suffix. Those method takes two floats representing the x,y coordinates of
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// the vector parameter and allow you to avoid to needlessly create a vector object :
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//
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// v2 = v1.add(new Vec2(3,4));
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// v2 = v1.add_xy(3,4); //equivalent to previous line
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//
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// angles are in radians by default but method that takes angle as parameters
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// or return angle values usually have a variant with a '_deg' suffix that works in degrees
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//
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// The 2D vector object
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function Vec2(x,y){
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this.x = x;
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this.y = y;
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}
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window.Vec2 = Vec2;
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// Multiply a number expressed in radiant by rad2deg to convert it in degrees
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var rad2deg = 57.29577951308232;
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// Multiply a number expressed in degrees by deg2rad to convert it to radiant
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var deg2rad = 0.017453292519943295;
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// The numerical precision used to compare vector equality
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var epsilon = 0.0000001;
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// This static method creates a new vector from polar coordinates with the angle expressed
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// in degrees
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Vec2.new_polar_deg = function(len,angle){
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var v = new Vec2(len,0);
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return v.rotate_deg(angle);
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};
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// This static method creates a new vector from polar coordinates with the angle expressed in
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// radians
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Vec2.new_polar = function(len,angle){
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var v = new Vec2(len,0);
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v.rotate(angle);
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return v;
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};
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// returns the length or modulus or magnitude of the vector
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Vec2.prototype.len = function(){
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return Math.sqrt(this.x*this.x + this.y*this.y);
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};
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// returns the squared length of the vector, this method is much faster than len()
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Vec2.prototype.len_sq = function(){
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return this.x*this.x + this.y*this.y;
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};
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// return the distance between this vector and the vector v
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Vec2.prototype.dist = function(v){
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var dx = this.x - v.x;
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var dy = this.y - v.y;
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return Math.sqrt(dx*dx + dy*dy);
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};
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// return the distance between this vector and the vector of coordinates (x,y)
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Vec2.prototype.dist_xy = function(x,y){
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var dx = this.x - x;
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var dy = this.y - y;
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return Math.sqrt(dx*dx + dy*dy);
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};
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// return the squared distance between this vector and the vector and the vector v
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Vec2.prototype.dist_sq = function(v){
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var dx = this.x - v.x;
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var dy = this.y - v.y;
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return dx*dx + dy*dy;
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};
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// return the squared distance between this vector and the vector of coordinates (x,y)
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Vec2.prototype.dist_sq_xy = function(x,y){
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var dx = this.x - x;
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var dy = this.y - y;
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return dx*dx + dy*dy;
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};
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// return the dot product between this vector and the vector v
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Vec2.prototype.dot = function(v){
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return this.x*v.x + this.y*v.y;
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};
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// return the dot product between this vector and the vector of coordinate (x,y)
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Vec2.prototype.dot_xy = function(x,y){
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return this.x*x + this.y*y;
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};
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// return a new vector with the same coordinates as this
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Vec2.prototype.clone = function(){
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return new Vec2(this.x,this.y);
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};
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// return the sum of this and vector v as a new vector
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Vec2.prototype.add = function(v){
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return new Vec2(this.x+v.x,this.y+v.y);
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};
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// return the sum of this and vector (x,y) as a new vector
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Vec2.prototype.add_xy = function(x,y){
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return new Vec2(this.x+x,this.y+y);
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};
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// returns (this - v) as a new vector where v is a vector and - is the vector subtraction
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Vec2.prototype.sub = function(v){
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return new Vec2(this.x-v.x,this.y-v.y);
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};
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// returns (this - (x,y)) as a new vector where - is vector subtraction
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Vec2.prototype.sub_xy = function(x,y){
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return new Vec2(this.x-x,this.y-y);
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};
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// return (this * v) as a new vector where v is a vector and * is the by component product
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Vec2.prototype.mult = function(v){
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return new Vec2(this.x*v.x,this.y*v.y);
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};
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// return (this * (x,y)) as a new vector where * is the by component product
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Vec2.prototype.mult_xy = function(x,y){
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return new Vec2(this.x*x,this.y*y);
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};
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// return this scaled by float f as a new fector
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Vec2.prototype.scale = function(f){
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return new Vec2(this.x*f, this.y*f);
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};
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// return the negation of this vector
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Vec2.prototype.neg = function(f){
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return new Vec2(-this.x,-this.y);
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};
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// return this vector normalized as a new vector
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Vec2.prototype.normalize = function(){
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var len = this.len();
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if(len == 0){
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return new Vec2(0,1);
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}else if(len != 1){
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return this.scale(1.0/len);
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}
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return new Vec2(this.x,this.y);
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};
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// return a new vector with the same direction as this vector of length float l. (negative values of l will invert direction)
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Vec2.prototype.set_len = function(l){
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return this.normalize().scale(l);
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};
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// return the projection of this onto the vector v as a new vector
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Vec2.prototype.project = function(v){
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return v.set_len(this.dot(v));
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};
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// return a string representation of this vector
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Vec2.prototype.toString = function(){
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var str = "";
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str += "[";
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str += this.x;
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str += ",";
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str += this.y;
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str += "]";
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return str;
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};
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//return this vector counterclockwise rotated by rad radians as a new vector
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Vec2.prototype.rotate = function(rad){
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var c = Math.cos(rad);
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var s = Math.sin(rad);
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var px = this.x * c - this.y *s;
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var py = this.x * s + this.y *c;
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return new Vec2(px,py);
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};
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//return this vector counterclockwise rotated by deg degrees as a new vector
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Vec2.prototype.rotate_deg = function(deg){
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return this.rotate(deg * deg2rad);
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};
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//linearly interpolate this vector towards the vector v by float factor alpha.
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// alpha == 0 : does nothing
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// alpha == 1 : sets this to v
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Vec2.prototype.lerp = function(v,alpha){
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var inv_alpha = 1 - alpha;
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return new Vec2( this.x * inv_alpha + v.x * alpha,
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this.y * inv_alpha + v.y * alpha );
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};
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// returns the angle between this vector and the vector (1,0) in radians
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Vec2.prototype.angle = function(){
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return Math.atan2(this.y,this.x);
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};
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// returns the angle between this vector and the vector (1,0) in degrees
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Vec2.prototype.angle_deg = function(){
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return Math.atan2(this.y,this.x) * rad2deg;
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};
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// returns true if this vector is equal to the vector v, with a tolerance defined by the epsilon module constant
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Vec2.prototype.equals = function(v){
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if(Math.abs(this.x-v.x) > epsilon){
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return false;
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}else if(Math.abs(this.y-v.y) > epsilon){
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return false;
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}
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return true;
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};
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// returns true if this vector is equal to the vector (x,y) with a tolerance defined by the epsilon module constant
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Vec2.prototype.equals_xy = function(x,y){
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if(Math.abs(this.x-x) > epsilon){
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return false;
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}else if(Math.abs(this.y-y) > epsilon){
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return false;
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}
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return true;
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};
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})(window);
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(function(window){
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// A Bounding Shapes Library
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// A Bounding Ellipse
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// cx,cy : center of the ellipse
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// rx,ry : radius of the ellipse
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function BEllipse(cx,cy,rx,ry){
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this.type = 'ellipse';
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this.x = cx-rx; // minimum x coordinate contained in the ellipse
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this.y = cy-ry; // minimum y coordinate contained in the ellipse
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this.sx = 2*rx; // width of the ellipse on the x axis
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this.sy = 2*ry; // width of the ellipse on the y axis
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this.hx = rx; // half of the ellipse width on the x axis
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this.hy = ry; // half of the ellipse width on the y axis
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this.cx = cx; // x coordinate of the ellipse center
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this.cy = cy; // y coordinate of the ellipse center
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this.mx = cx + rx; // maximum x coordinate contained in the ellipse
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this.my = cy + ry; // maximum x coordinate contained in the ellipse
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}
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window.BEllipse = BEllipse;
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// returns an unordered list of vector defining the positions of the intersections between the ellipse's
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// boundary and a line segment defined by the start and end vectors a,b
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BEllipse.prototype.collide_segment = function(a,b){
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// http://paulbourke.net/geometry/sphereline/
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var collisions = [];
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if(a.equals(b)){ //we do not compute the intersection in this case. TODO ?
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return collisions;
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}
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// make all computations in a space where the ellipse is a circle
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// centered on zero
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var c = new Vec2(this.cx,this.cy);
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a = a.sub(c).mult_xy(1/this.hx,1/this.hy);
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b = b.sub(c).mult_xy(1/this.hx,1/this.hy);
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if(a.len_sq() < 1 && b.len_sq() < 1){ //both points inside the ellipse
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return collisions;
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}
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// compute the roots of the intersection
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var ab = b.sub(a);
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var A = (ab.x*ab.x + ab.y*ab.y);
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var B = 2*( ab.x*a.x + ab.y*a.y);
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var C = a.x*a.x + a.y*a.y - 1;
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var u = B * B - 4*A*C;
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if(u < 0){
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return collisions;
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}
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u = Math.sqrt(u);
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var u1 = (-B + u) / (2*A);
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var u2 = (-B - u) / (2*A);
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if(u1 >= 0 && u1 <= 1){
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var pos = a.add(ab.scale(u1));
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collisions.push(pos);
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}
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if(u1 != u2 && u2 >= 0 && u2 <= 1){
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var pos = a.add(ab.scale(u2));
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collisions.push(pos);
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}
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for(var i = 0; i < collisions.length; i++){
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collisions[i] = collisions[i].mult_xy(this.hx,this.hy);
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collisions[i] = collisions[i].add_xy(this.cx,this.cy);
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}
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return collisions;
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};
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// A bounding rectangle
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// x,y the minimum coordinate contained in the rectangle
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// sx,sy the size of the rectangle along the x,y axis
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function BRect(x,y,sx,sy){
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this.type = 'rect';
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this.x = x; // minimum x coordinate contained in the rectangle
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this.y = y; // minimum y coordinate contained in the rectangle
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this.sx = sx; // width of the rectangle on the x axis
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this.sy = sy; // width of the rectangle on the y axis
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this.hx = sx/2; // half of the rectangle width on the x axis
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this.hy = sy/2; // half of the rectangle width on the y axis
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this.cx = x + this.hx; // x coordinate of the rectangle center
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this.cy = y + this.hy; // y coordinate of the rectangle center
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this.mx = x + sx; // maximum x coordinate contained in the rectangle
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this.my = y + sy; // maximum x coordinate contained in the rectangle
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}
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window.BRect = BRect;
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// Static method creating a new bounding rectangle of size (sx,sy) centered on (cx,cy)
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BRect.new_centered = function(cx,cy,sx,sy){
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return new BRect(cx-sx/2,cy-sy/2,sx,sy);
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};
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//intersect line a,b with line c,d, returns null if no intersection
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function line_intersect(a,b,c,d){
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// http://paulbourke.net/geometry/lineline2d/
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var f = ((d.y - c.y)*(b.x - a.x) - (d.x - c.x)*(b.y - a.y));
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if(f == 0){
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return null;
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}
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f = 1 / f;
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var fab = ((d.x - c.x)*(a.y - c.y) - (d.y - c.y)*(a.x - c.x)) * f ;
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if(fab < 0 || fab > 1){
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return null;
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}
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var fcd = ((b.x - a.x)*(a.y - c.y) - (b.y - a.y)*(a.x - c.x)) * f ;
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if(fcd < 0 || fcd > 1){
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return null;
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}
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return new Vec2(a.x + fab * (b.x-a.x), a.y + fab * (b.y - a.y) );
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}
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// returns an unordered list of vector defining the positions of the intersections between the ellipse's
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// boundary and a line segment defined by the start and end vectors a,b
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BRect.prototype.collide_segment = function(a,b){
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var collisions = [];
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var corners = [ new Vec2(this.x,this.y), new Vec2(this.x,this.my),
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new Vec2(this.mx,this.my), new Vec2(this.mx,this.y) ];
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var pos = line_intersect(a,b,corners[0],corners[1]);
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if(pos) collisions.push(pos);
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pos = line_intersect(a,b,corners[1],corners[2]);
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if(pos) collisions.push(pos);
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pos = line_intersect(a,b,corners[2],corners[3]);
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if(pos) collisions.push(pos);
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pos = line_intersect(a,b,corners[3],corners[0]);
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if(pos) collisions.push(pos);
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return collisions;
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};
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// returns true if the rectangle contains the position defined by the vector 'vec'
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BRect.prototype.contains_vec = function(vec){
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return ( vec.x >= this.x && vec.x <= this.mx &&
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vec.y >= this.y && vec.y <= this.my );
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};
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// returns true if the rectangle contains the position (x,y)
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BRect.prototype.contains_xy = function(x,y){
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return ( x >= this.x && x <= this.mx &&
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y >= this.y && y <= this.my );
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};
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// returns true if the ellipse contains the position defined by the vector 'vec'
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BEllipse.prototype.contains_vec = function(v){
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v = v.mult_xy(this.hx,this.hy);
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return v.len_sq() <= 1;
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};
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// returns true if the ellipse contains the position (x,y)
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BEllipse.prototype.contains_xy = function(x,y){
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return this.contains(new Vec2(x,y));
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};
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})(window);
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