A formula for bouncing and a formula for detecting rectangular boundaries

Important formula:

(1) Simple slow motion

DX = targetx-object.x;

dy = Targety-object.y;

VX = dx * easing;

VY = dy * easing;

Object.x + = VX;

Object.y + = VY;

Can be streamlined:

VX = (targetx-object.x) * easing;

VY = (targety-object.y) * easing;

Object.x + = VX;

Object.y + = VY;

Further streamlining:

Object.x + = (targetx-object.x) * easing;

Object.y + = (targety-object.y) * easing;

(2) Simple elastic Motion

Ax = (targetx-object.x) * SPRING;

ay = (targety-object.y) * SPRING;

VX + = ax;

Vy + = ay;

VX *= friction;

VY *= Friction;

Object.x + = VX;

Object.y + = VY;

Can be streamlined:

VX + = (targetx-object.x) * SPRING;

VY + = (targety-object.y) * SPRING;

VX *= friction;

VY *= Friction;

Object.x + = VX;

Object.y + = VY;

Further streamlining:

VX + = (targetx-object.x) * SPRING;

VY + = (targety-object.y) * SPRING;

Object.x + = (VX *= friction);

Object.y + = (vy *= friction);

(3) An offset of the elastic motion

DX = Object.x-fixedx;

dy = object.y-fixedy;

Targetx = Fixedx + math.cos (angle) * SPRINGLENGTH;

Targety = Fixedy + math.sin (angle) * SPRINGLENGTH;

Important formula for boundary detection:

(1) Rectangular boundary collision detection

tool.intersects = function (bodya,bodyb) {

return! (bodya.x + bodya.width < bodyb.x | |

bodyb.x + bodyb.width < bodya.x | |

BODYA.Y + bodya.height < BODYB.Y | |

Bodyb.y + bodyb.height < BODYA.Y);

};

(2) Distance-based collision detection

DX = objectb.x-objecta.x;

dy = objectb.y-objecta.y;

Dist = math.sqrt (dx * dx + dy * dy);

if (Dist < Objecta.radius + Objectb.radius) {}

(3) Multi-object Collision detection

for (var i = 0; i < objects.length; i++) {

var objecta = objects[i];

For (var j = i + 1; j < Objects.length; J + +) {

var OBJECTB = objects[j];

if (tool.intersects (OBJECTA,OBJECTB) {}

}

};

A formula for bouncing and a formula for detecting rectangular boundaries