package Interpolation
import Wurstunit

// Credits to BlinkyBoy
/**Look at linear*/
public function linear(vec2 start, vec2 stop, real p) returns vec2
	return vec2(linear(start.x, stop.x, p), linear(start.y, stop.y, p))

public function bezier_3(vec2 start, vec2 mid, vec2 stop, real p) returns vec2
	return vec2(bezier_3(start.x, mid.x, stop.x, p), bezier_3(start.y, mid.y, stop.y, p))

/**
	Linear Interpolation
	Sample Usage:
	AddSpecialEffect(TEST_SFX,linear(P1X,P2X,p),linear(P1Y,P2Y,p))
*/
public function linear( real start, real stop, real p ) returns real
	return start + (stop-start)*p

/**
	3-Point-Bezier Interpolation
	Sample Usage:
	AddSpecialEffect(TEST_SFX,bezier_3(P1X,P3X,P2X,p),bezier_3(P1Y,P3Y,P2Y,p))
*/
public function bezier_3( real start, real mid, real stop, real p ) returns real
	return start + 2.*(mid-start)*p + (stop -2.*mid + start)*p*p


/**
	This function returns the derivate of the 3-Point-Bezier curve on certain point.
	(d(bezier_3())/dt)
*/
public function derivBezier_3( real start, real mid, real stop, real p ) returns real
	return 2.*(mid-start) + 2.*(stop-2.*mid+start)*p


/**
	4-Point-Bezier Interpolation
	Sample Usage:
	AddSpecialEffect(TEST_SFX,bezier_4(P1X,P3X,P4X,P2X,t),bezier_4(P1Y,P3Y,P4Y,P2Y,t))
*/
function bezier_4( real start, real mid1, real mid2, real stop, real p ) returns real
	real m = p*p
	return  start + 3.*p*(mid1 - start) + 3.*m*(mid2 - 2.*mid1 + start) + m*p*(3.*(mid1-mid2) + stop - start)

/**
	This function returns the derivate of the 4-Point-Bezier curve on certain point.
	(d(bezier_4())/dt)
*/
public function derivBezier_4( real start, real mid1, real mid2, real stop, real p ) returns real
	return 3.*(mid1-start) + 6.*(mid2-2.*mid1+start)*p + 3.*(3.*(mid1-mid2) + stop -start)*p*p


//You can use Bezier 3 to graphic perfect parabolas
//Bezier_4(<Start Point>, <OutTan_of_StartPoint>, <InTan_of_EndPoint>, <EndPoint>)

/**	Hermite Interpolation */
public function hermite( real start, real stop, real tangent1, real tangent2, real s ) returns real
	real s2 = s*s
	real h1 = 8.0*s*s2 - 9.0*s2
	real h2 = h1*(-1)
	real h3 = s2*(s - 2.0) + s
	real h4 = s2*(s - 1.0)
	h1 = h1 + 1
	return h1*start + h2*stop + h3*tangent1 + h4*tangent2



// TCB functions for finding the tangents among 3 points
// Most modellers may know TCB from 3dsmax, in which they are used to make rotations
// look very smooth.
// p = tension, c = continuity, b = bias
// tension is how sharply the curve makes turns.
// continuity specifies the rate of change between speed and direction.
// bias specifies the direction of the curve.
// sidenote: specify p1 as 0, when working with 2 points.

/** Returns the intan of p2 */
public function inTan( real p1, real p2, real p3, real p, real c, real b ) returns real
	return (1.0-p)*(1.0-c)*(1.0+b)*(p2-p1)/2. + (1.0-p)*(1.0+c)*(1.0-b)*(p3-p2)/2.


/** Returns the outtan of p2 */
public function outTan( real p1, real p2, real p3, real p, real c, real b ) returns real
	return (1.0-p)*(1.0+c)*(1.0+b)*(p2-p1)/2. + (1.0-p)*(1.0-c)*(1.0-b)*(p3-p2)/2.

public function axiAngle( real dy, real dx ) returns real
	return Atan2(dy,dx)

public function getCardTan( real p1, real p3 ) returns real
	return 0.5*(p3-p1)


@test function linearVecTest()
	let v = linear(vec2(3,4), vec2(6,2), 0.5)
	v.x.assertEquals(4.5, .001)
	v.y.assertEquals(3, .001)