/**
* Biltong v0.2
*
* Various geometry functions written as part of jsPlumb and perhaps useful for others.
*
* Copyright (c) 2014 Simon Porritt
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
* HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
* OTHER DEALINGS IN THE SOFTWARE.
*/
;(function() {
"use strict";
var Biltong = this.Biltong = {};
var _isa = function(a) { return Object.prototype.toString.call(a) === "[object Array]"; },
_pointHelper = function(p1, p2, fn) {
p1 = _isa(p1) ? p1 : [p1.x, p1.y];
p2 = _isa(p2) ? p2 : [p2.x, p2.y];
return fn(p1, p2);
},
/**
* @name Biltong.gradient
* @function
* @desc Calculates the gradient of a line between the two points.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Float} The gradient of a line between the two points.
*/
_gradient = Biltong.gradient = function(p1, p2) {
return _pointHelper(p1, p2, function(_p1, _p2) {
if (_p2[0] == _p1[0])
return _p2[1] > _p1[1] ? Infinity : -Infinity;
else if (_p2[1] == _p1[1])
return _p2[0] > _p1[0] ? 0 : -0;
else
return (_p2[1] - _p1[1]) / (_p2[0] - _p1[0]);
});
},
/**
* @name Biltong.normal
* @function
* @desc Calculates the gradient of a normal to a line between the two points.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Float} The gradient of a normal to a line between the two points.
*/
_normal = Biltong.normal = function(p1, p2) {
return -1 / _gradient(p1, p2);
},
/**
* @name Biltong.lineLength
* @function
* @desc Calculates the length of a line between the two points.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Float} The length of a line between the two points.
*/
_lineLength = Biltong.lineLength = function(p1, p2) {
return _pointHelper(p1, p2, function(_p1, _p2) {
return Math.sqrt(Math.pow(_p2[1] - _p1[1], 2) + Math.pow(_p2[0] - _p1[0], 2));
});
},
/**
* @name Biltong.quadrant
* @function
* @desc Calculates the quadrant in which the angle between the two points lies.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Integer} The quadrant - 1 for upper right, 2 for lower right, 3 for lower left, 4 for upper left.
*/
_quadrant = Biltong.quadrant = function(p1, p2) {
return _pointHelper(p1, p2, function(_p1, _p2) {
if (_p2[0] > _p1[0]) {
return (_p2[1] > _p1[1]) ? 2 : 1;
}
else if (_p2[0] == _p1[0]) {
return _p2[1] > _p1[1] ? 2 : 1;
}
else {
return (_p2[1] > _p1[1]) ? 3 : 4;
}
});
},
/**
* @name Biltong.theta
* @function
* @desc Calculates the angle between the two points.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Float} The angle between the two points.
*/
_theta = Biltong.theta = function(p1, p2) {
return _pointHelper(p1, p2, function(_p1, _p2) {
var m = _gradient(_p1, _p2),
t = Math.atan(m),
s = _quadrant(_p1, _p2);
if ((s == 4 || s== 3)) t += Math.PI;
if (t < 0) t += (2 * Math.PI);
return t;
});
},
/**
* @name Biltong.intersects
* @function
* @desc Calculates whether or not the two rectangles intersect.
* @param {Rectangle} r1 First rectangle, as a js object in the form `{x:.., y:.., w:.., h:..}`
* @param {Rectangle} r2 Second rectangle, as a js object in the form `{x:.., y:.., w:.., h:..}`
* @return {Boolean} True if the rectangles intersect, false otherwise.
*/
_intersects = Biltong.intersects = function(r1, r2) {
var x1 = r1.x, x2 = r1.x + r1.w, y1 = r1.y, y2 = r1.y + r1.h,
a1 = r2.x, a2 = r2.x + r2.w, b1 = r2.y, b2 = r2.y + r2.h;
return ( (x1 <= a1 && a1 <= x2) && (y1 <= b1 && b1 <= y2) ) ||
( (x1 <= a2 && a2 <= x2) && (y1 <= b1 && b1 <= y2) ) ||
( (x1 <= a1 && a1 <= x2) && (y1 <= b2 && b2 <= y2) ) ||
( (x1 <= a2 && a1 <= x2) && (y1 <= b2 && b2 <= y2) ) ||
( (a1 <= x1 && x1 <= a2) && (b1 <= y1 && y1 <= b2) ) ||
( (a1 <= x2 && x2 <= a2) && (b1 <= y1 && y1 <= b2) ) ||
( (a1 <= x1 && x1 <= a2) && (b1 <= y2 && y2 <= b2) ) ||
( (a1 <= x2 && x1 <= a2) && (b1 <= y2 && y2 <= b2) );
},
/**
* @name Biltong.encloses
* @function
* @desc Calculates whether or not r2 is completely enclosed by r1.
* @param {Rectangle} r1 First rectangle, as a js object in the form `{x:.., y:.., w:.., h:..}`
* @param {Rectangle} r2 Second rectangle, as a js object in the form `{x:.., y:.., w:.., h:..}`
* @param {Boolean} [allowSharedEdges=false] If true, the concept of enclosure allows for one or more edges to be shared by the two rectangles.
* @return {Boolean} True if r1 encloses r2, false otherwise.
*/
_encloses = Biltong.encloses = function(r1, r2, allowSharedEdges) {
var x1 = r1.x, x2 = r1.x + r1.w, y1 = r1.y, y2 = r1.y + r1.h,
a1 = r2.x, a2 = r2.x + r2.w, b1 = r2.y, b2 = r2.y + r2.h,
c = function(v1, v2, v3, v4) { return allowSharedEdges ? v1 <= v2 && v3>= v4 : v1 < v2 && v3 > v4; };
return c(x1,a1,x2,a2) && c(y1,b1,y2,b2);
},
_segmentMultipliers = [null, [1, -1], [1, 1], [-1, 1], [-1, -1] ],
_inverseSegmentMultipliers = [null, [-1, -1], [-1, 1], [1, 1], [1, -1] ],
/**
* @name Biltong.pointOnLine
* @function
* @desc Calculates a point on the line from `fromPoint` to `toPoint` that is `distance` units along the length of the line.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Point} Point on the line, in the form `{ x:..., y:... }`.
*/
_pointOnLine = Biltong.pointOnLine = function(fromPoint, toPoint, distance) {
var m = _gradient(fromPoint, toPoint),
s = _quadrant(fromPoint, toPoint),
segmentMultiplier = distance > 0 ? _segmentMultipliers[s] : _inverseSegmentMultipliers[s],
theta = Math.atan(m),
y = Math.abs(distance * Math.sin(theta)) * segmentMultiplier[1],
x = Math.abs(distance * Math.cos(theta)) * segmentMultiplier[0];
return { x:fromPoint.x + x, y:fromPoint.y + y };
},
/**
* @name Biltong.perpendicularLineTo
* @function
* @desc Calculates a line of length `length` that is perpendicular to the line from `fromPoint` to `toPoint` and passes through `toPoint`.
* @param {Point} p1 First point, either as a 2 entry array or object with `left` and `top` properties.
* @param {Point} p2 Second point, either as a 2 entry array or object with `left` and `top` properties.
* @return {Line} Perpendicular line, in the form `[ { x:..., y:... }, { x:..., y:... } ]`.
*/
_perpendicularLineTo = Biltong.perpendicularLineTo = function(fromPoint, toPoint, length) {
var m = _gradient(fromPoint, toPoint),
theta2 = Math.atan(-1 / m),
y = length / 2 * Math.sin(theta2),
x = length / 2 * Math.cos(theta2);
return [{x:toPoint.x + x, y:toPoint.y + y}, {x:toPoint.x - x, y:toPoint.y - y}];
};
}).call(this);