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Algebra.hx
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package trilateral.geom;
import trilateral.tri.Triangle;
import trilateral.geom.Point;
import trilateral.tri.Trilateral;
import trilateral.tri.TrilateralPair;
import trilateral.angle.Fraction;
import trilateral.angle.Pi2pi;
import trilateral.angle.ZeroTo2pi;
typedef QuadPoint = { A: Point, B: Point, C: Point, D: Point };
class Algebra {
public inline static
function theta( p0: Point, p1: Point ): Float {
var dx: Float = p0.x - p1.x;
var dy: Float = p0.y - p1.y;
return Math.atan2( dy, dx );
}
public static inline
function dist( p0: Point, p1: Point ): Float {
var dx: Float = p0.x - p1.x;
var dy: Float = p0.y - p1.y;
return dx*dx + dy*dy;
}
// A B C, you can find the winding by computing the cross product (B - A) x (C - A)
public static inline
function adjustWinding( A_: Point, B_: Point, C_: Point ): Bool{
var val: Bool = !( cross( subtract( B_, A_ ), subtract( C_, A_ ) ) < 0 );
return val;
}
// subtract
public static inline
function subtract( p0: Point, p1: Point ) : Point {
return { x: p0.x - p1.x, y: p0.y - p1.y };
}
// to get the cross product
public static inline
function cross( p0: Point, p1: Point ) : Float {
return p0.x*p1.y - p0.y*p1.x;
}
public static inline
function sign( n: Float ): Int {
return Std.int( Math.abs( n )/n );
}
//Bezier
public static inline
function quadratic ( t: Float, s: Float, c: Float, e: Float ): Float {
var u = 1 - t;
return Math.pow( u, 2 )*s + 2*u*t*c + Math.pow( t, 2 )*e;
}
public static inline
function cubic( t: Float, s: Float, c1: Float, c2: Float, e: Float ): Float {
var u = 1 - t;
return Math.pow( u, 3 )*s + 3*Math.pow( u, 2 )*t*c1 + 3*u*Math.pow( t, 2 )*c2 + Math.pow( t, 3 )*e;
}
public static
var quadStep: Float = 0.03;
// Create Quadratic Curve
public static inline
function quadCurve( p: Array<Float>, ax: Float, ay: Float, bx: Float, by: Float, cx: Float, cy: Float ): Array<Float> {
var step = calculateQuadStep( ax, ay, bx, by, cx, cy );
var l = p.length;
p[ l++ ] = ax;
p[ l++ ] = ay;
var t = step;
while( t < 1. ){
p[ l++ ] = quadratic( t, ax, bx, cx );
p[ l++ ] = quadratic( t, ay, by, cy );
t += step;
}
p[ l++ ] = cx;
p[ l++ ] = cy;
return p;
}
public static
var cubicStep: Float = 0.03;
// Create Cubic Curve
public static inline
function cubicCurve( p: Array<Float>, ax: Float, ay: Float, bx: Float, by: Float, cx: Float, cy: Float, dx: Float, dy: Float ): Array<Float> {
var step = calculateCubicStep( ax, ay, bx, by, cx, cy, dx, dy );
var l = p.length;
p[ l++ ] = ax;
p[ l++ ] = ay;
var t = step;
while( t < 1. ){
p[ l++ ] = cubic( t, ax, bx, cx, dx );
p[ l++ ] = cubic( t, ay, by, cy, dy );
t += step;
}
p[ l++ ] = dx;
p[ l++ ] = dy;
return p;
}
public static inline
function calculateQuadStep( ax: Float, ay: Float, bx: Float, by: Float, cx: Float, cy: Float ): Float {
var approxDistance = distance( ax, ay, bx, by ) + distance( bx, by, cx, cy );
if( approxDistance == 0 ) approxDistance = 0.000001;
return Math.min( 1/( approxDistance*0.707 ), quadStep );
}
public static inline
function calculateCubicStep( ax: Float, ay: Float, bx: Float, by: Float, cx: Float, cy: Float, dx: Float, dy: Float ): Float {
var approxDistance = distance( ax, ay, bx, by ) + distance( bx, by, cx, cy ) + distance( cx, cy, dx, dy );
if( approxDistance == 0 ) approxDistance = 0.000001;
return Math.min( 1/( approxDistance*0.707 ), cubicStep );
}
/* NOT STABLE ENOUGH :( - may remove soon!
public static inline
function eggPoints( p: Array<Float>, x: Float, y: Float, width: Float, ?sides: Int = 70 ){
var sidesHalf: Int = Std.int( sides/2 ) + 1;
var px: Float = 0;
var py: Float = 0;
var a = 5;
var b = 0.7*a;
var l = 0;
for( i in 0...Std.int( sides/2 ) ){
if( i != 0 ){
px = i/5;
py = Math.sqrt( px ) * Math.sqrt( Math.abs(
(a-b) -2*px + Math.sqrt( 4*b*px + Math.pow( a-b, 2 ) ) )
)/Math.sqrt( 2 );
//py = Math.sqrt(
// Math.abs( -20*Math.pow( px, 2 ) - px*Math.sqrt( 280*px + 9 ) + 3*px )
// )/( 2*Math.sqrt( 5 ) );
}
p[ Std.int( sides*2 ) - l ] = px*width + x;
p[ l ] = px*width + x;
l++;
p[ Std.int( sides*2 ) - l ] = -py*width + y;
p[ l ] = py*width + y;
l++;
}
}
*/
// may not be most optimal
public inline static
function lineAB( A: Point, B: Point, width: Float ){
var dx: Float = A.x - B.x;
var dy: Float = A.y - B.y;
var P = { x:A.x - width/2, y:A.y };
var omega = thetaCheap( dx, dy ); // may need angle correction.
var dim: Point = { x: width, y: distCheap( dx, dy ) };
return rotateVectorLine( P, dim, omega, A.x + width/2, A.y );
}
// may not be most optimal
public inline static
function lineABCoord( ax: Float, ay: Float, bx: Float, by: Float, width: Float ){
var dx: Float = ax - bx;
var dy: Float = ay - by;
var P = { x:ax - width/2, y:ay };
var omega = thetaCheap( dx, dy ); // may need angle correction.
var dim: Point = { x: width, y: distCheap( dx, dy ) };
return rotateVectorLine( P, dim, omega, ax + width/2, ay );
}
public inline static
function rotateVectorLine( pos: Point, dim: Point, omega: Float, pivotX: Float, pivotY: Float ): QuadPoint {
// A B
// D C
var px = pos.x;
var py = pos.y;
var dx = dim.x;
var dy = dim.y;
var A_ = { x: px, y: py };
var B_ = { x: px + dx, y: py };
var C_ = { x: px + dx, y: py + dy };
var D_ = { x: px, y: py + dy };
if( omega != 0. ){
var sin = Math.sin( omega );
var cos = Math.cos( omega );
A_ = Algebra.pivotCheap( A_, sin, cos, pivotX, pivotY );
B_ = Algebra.pivotCheap( B_, sin, cos, pivotX, pivotY );
C_ = Algebra.pivotCheap( C_, sin, cos, pivotX, pivotY );
D_ = Algebra.pivotCheap( D_, sin, cos, pivotX, pivotY );
}
return { A:A_, B:B_, C:C_, D:D_ };
}
public inline static
function pivotCheap( p: Point, sin: Float, cos: Float, pivotX: Float, pivotY: Float ){
var px = p.x - pivotX;
var py = p.y - pivotY;
var px2 = px * cos - py * sin;
py = py * cos + px * sin;
return { x: px2 + pivotX, y: py + pivotY };
}
public inline static // not used?
function pivot( p: Point, omega: Float, pivotX: Float, pivotY: Float ){
var px = p.x - pivotX;
var py = p.y - pivotY;
var px2 = px * Math.cos( omega ) - py * Math.sin( omega );
py = py * Math.cos( omega ) + px * Math.sin( omega );
return { x: px2 + pivotX, y: py + pivotY };
}
public inline static
function thetaCheap( dx: Float, dy: Float ): Float {
return Math.atan2( dy, dx );
}
public static inline
function distCheap( dx: Float, dy: Float ): Float {
return dx*dx + dy*dy;
}
public static inline
function distance( px: Float, py: Float, qx: Float, qy: Float ): Float {
var x = px - qx;
var y = py - qy;
return Math.sqrt( x*x + y*y );
}
}