phaser
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A fast, free and fun HTML5 Game Framework for Desktop and Mobile web browsers.
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JavaScript
/**
* The `Matter.SAT` module contains methods for detecting collisions using the Separating Axis Theorem.
*
* @class SAT
*/
// TODO: true circles and curves
var SAT = {};
module.exports = SAT;
var Vertices = require('../geometry/Vertices');
var Vector = require('../geometry/Vector');
(function() {
/**
* Detect collision between two bodies using the Separating Axis Theorem.
* @method collides
* @param {body} bodyA
* @param {body} bodyB
* @param {collision} previousCollision
* @return {collision} collision
*/
SAT.collides = function(bodyA, bodyB, previousCollision) {
var overlapAB,
overlapBA,
minOverlap,
collision,
canReusePrevCol = false;
if (previousCollision) {
// estimate total motion
var parentA = bodyA.parent,
parentB = bodyB.parent,
motion = parentA.speed * parentA.speed + parentA.angularSpeed * parentA.angularSpeed
+ parentB.speed * parentB.speed + parentB.angularSpeed * parentB.angularSpeed;
// we may be able to (partially) reuse collision result
// but only safe if collision was resting
canReusePrevCol = previousCollision && previousCollision.collided && motion < 0.2;
// reuse collision object
collision = previousCollision;
} else {
collision = { collided: false, bodyA: bodyA, bodyB: bodyB };
}
if (previousCollision && canReusePrevCol) {
// if we can reuse the collision result
// we only need to test the previously found axis
var axisBodyA = collision.axisBody,
axisBodyB = axisBodyA === bodyA ? bodyB : bodyA,
axes = [axisBodyA.axes[previousCollision.axisNumber]];
minOverlap = _overlapAxes(axisBodyA.vertices, axisBodyB.vertices, axes);
collision.reused = true;
if (minOverlap.overlap <= 0) {
collision.collided = false;
return collision;
}
} else {
// if we can't reuse a result, perform a full SAT test
overlapAB = _overlapAxes(bodyA.vertices, bodyB.vertices, bodyA.axes);
if (overlapAB.overlap <= 0) {
collision.collided = false;
return collision;
}
overlapBA = _overlapAxes(bodyB.vertices, bodyA.vertices, bodyB.axes);
if (overlapBA.overlap <= 0) {
collision.collided = false;
return collision;
}
if (overlapAB.overlap < overlapBA.overlap) {
minOverlap = overlapAB;
collision.axisBody = bodyA;
} else {
minOverlap = overlapBA;
collision.axisBody = bodyB;
}
// important for reuse later
collision.axisNumber = minOverlap.axisNumber;
}
collision.bodyA = bodyA.id < bodyB.id ? bodyA : bodyB;
collision.bodyB = bodyA.id < bodyB.id ? bodyB : bodyA;
collision.collided = true;
collision.depth = minOverlap.overlap;
collision.parentA = collision.bodyA.parent;
collision.parentB = collision.bodyB.parent;
bodyA = collision.bodyA;
bodyB = collision.bodyB;
// ensure normal is facing away from bodyA
if (Vector.dot(minOverlap.axis, Vector.sub(bodyB.position, bodyA.position)) < 0) {
collision.normal = {
x: minOverlap.axis.x,
y: minOverlap.axis.y
};
} else {
collision.normal = {
x: -minOverlap.axis.x,
y: -minOverlap.axis.y
};
}
collision.tangent = Vector.perp(collision.normal);
collision.penetration = collision.penetration || {};
collision.penetration.x = collision.normal.x * collision.depth;
collision.penetration.y = collision.normal.y * collision.depth;
// find support points, there is always either exactly one or two
var verticesB = _findSupports(bodyA, bodyB, collision.normal),
supports = [];
// find the supports from bodyB that are inside bodyA
if (Vertices.contains(bodyA.vertices, verticesB[0]))
supports.push(verticesB[0]);
if (Vertices.contains(bodyA.vertices, verticesB[1]))
supports.push(verticesB[1]);
// find the supports from bodyA that are inside bodyB
if (supports.length < 2) {
var verticesA = _findSupports(bodyB, bodyA, Vector.neg(collision.normal));
if (Vertices.contains(bodyB.vertices, verticesA[0]))
supports.push(verticesA[0]);
if (supports.length < 2 && Vertices.contains(bodyB.vertices, verticesA[1]))
supports.push(verticesA[1]);
}
// account for the edge case of overlapping but no vertex containment
if (supports.length < 1)
supports = [verticesB[0]];
collision.supports = supports;
return collision;
};
/**
* Find the overlap between two sets of vertices.
* @method _overlapAxes
* @private
* @param {} verticesA
* @param {} verticesB
* @param {} axes
* @return result
*/
var _overlapAxes = function(verticesA, verticesB, axes) {
var projectionA = Vector._temp[0],
projectionB = Vector._temp[1],
result = { overlap: Number.MAX_VALUE },
overlap,
axis;
for (var i = 0; i < axes.length; i++) {
axis = axes[i];
_projectToAxis(projectionA, verticesA, axis);
_projectToAxis(projectionB, verticesB, axis);
overlap = Math.min(projectionA.max - projectionB.min, projectionB.max - projectionA.min);
if (overlap <= 0) {
result.overlap = overlap;
return result;
}
if (overlap < result.overlap) {
result.overlap = overlap;
result.axis = axis;
result.axisNumber = i;
}
}
return result;
};
/**
* Projects vertices on an axis and returns an interval.
* @method _projectToAxis
* @private
* @param {} projection
* @param {} vertices
* @param {} axis
*/
var _projectToAxis = function(projection, vertices, axis) {
var min = Vector.dot(vertices[0], axis),
max = min;
for (var i = 1; i < vertices.length; i += 1) {
var dot = Vector.dot(vertices[i], axis);
if (dot > max) {
max = dot;
} else if (dot < min) {
min = dot;
}
}
projection.min = min;
projection.max = max;
};
/**
* Finds supporting vertices given two bodies along a given direction using hill-climbing.
* @method _findSupports
* @private
* @param {} bodyA
* @param {} bodyB
* @param {} normal
* @return [vector]
*/
var _findSupports = function(bodyA, bodyB, normal) {
var nearestDistance = Number.MAX_VALUE,
vertexToBody = Vector._temp[0],
vertices = bodyB.vertices,
bodyAPosition = bodyA.position,
distance,
vertex,
vertexA,
vertexB;
// find closest vertex on bodyB
for (var i = 0; i < vertices.length; i++) {
vertex = vertices[i];
vertexToBody.x = vertex.x - bodyAPosition.x;
vertexToBody.y = vertex.y - bodyAPosition.y;
distance = -Vector.dot(normal, vertexToBody);
if (distance < nearestDistance) {
nearestDistance = distance;
vertexA = vertex;
}
}
// find next closest vertex using the two connected to it
var prevIndex = vertexA.index - 1 >= 0 ? vertexA.index - 1 : vertices.length - 1;
vertex = vertices[prevIndex];
vertexToBody.x = vertex.x - bodyAPosition.x;
vertexToBody.y = vertex.y - bodyAPosition.y;
nearestDistance = -Vector.dot(normal, vertexToBody);
vertexB = vertex;
var nextIndex = (vertexA.index + 1) % vertices.length;
vertex = vertices[nextIndex];
vertexToBody.x = vertex.x - bodyAPosition.x;
vertexToBody.y = vertex.y - bodyAPosition.y;
distance = -Vector.dot(normal, vertexToBody);
if (distance < nearestDistance) {
vertexB = vertex;
}
return [vertexA, vertexB];
};
})();