// title: Geometry classes
// author: olafhochherz
// description:
// This are Classes I am working on to develop a nice Geometry Quark ... one day ... a you need VectorSpace Quark for this
// code:
LineND{
	var <>positionVector,<>directionVector,<>segment;
	*new { arg positionVector,directionVector,segment=false;
		^super.newCopyArgs(positionVector,directionVector,segment);
	}
	*newUsingPoints{arg positionVector1,positionVector2,segment=false;
		^super.newCopyArgs(positionVector1,(positionVector2-positionVector1),segment);
	}

	projectPoint2Line{arg aPoint;
		^positionVector+directionVector.proj(aPoint-positionVector);
	}
	projectPoint2Segment{arg aPoint;
		var cp=positionVector+directionVector.proj(aPoint-positionVector);
		var o=LineND(aPoint,cp-aPoint);
		^this.intersection(o);
	}

	isOrthogonal{arg aLine; ^directionVector.isOrthogonal(aLine.directionVector);}

	isParallel{arg aLine;
		var a=this.directionVector.angle(aLine.directionVector);
		if((a==pi)||(a==0),{^true},{^false});
	}

	skewLinesNearestPoints{arg aLine;
		var p1 = this.positionVector;
		var p2 =  aLine.positionVector;
		var d1 = this.directionVector;
		var d2 =  aLine.directionVector;
		var delta = (sum(d1**2)*sum(d2**2)) - ((d1 <|> d2)**2);
		var delta1 = ((d2<|> (p1-p2)) * (d1<|> d2)) - ((d1<|> (p1-p2)) * sum(d2**2));
		var delta2 = ((d2<|> (p1-p2)) * sum(d1**2)) - ((d1<|> d2) * (d1<|> (p1-p2)));
		var t1 = delta1 / delta;
		var t2 = delta2 / delta;


		if (this.segment, {
			t1=t1.min(1).max(0);
		});
		if (aLine.segment, {
			t2.min(1).max(0);
		});
		^[p1+(t1*d1), p2+(t2*d2)];
	}

	intersection{arg aLine;
		var p1,p2;
		#p1,p2 = this.skewLinesNearestPoints(aLine);
		if(p1.dist(p2)<0.00001,{^p1},{^false});
	}

	prPointAt{arg index,value;
		var r=(value/directionVector[index])-(positionVector[index]/directionVector[index]);
		^this.getPointOnLine(r);
	}

	getPointOnLine{arg s;
		^(this.positionVector+(s*this.directionVector));
	}
}

Plane{
	var <>positionVector,<>spanA,<>spanB;
	*new { arg positionVector,spanA,spanB;
		^super.newCopyArgs(positionVector,
			spanA,
			spanB)
	}

	*newUsingPoints{arg positionVector1,positionVector2,positionVector3;
		^super.newCopyArgs(positionVector1,
			(positionVector2-positionVector1),
			(positionVector3-positionVector1));
	}

	prProjectionScalars{arg aPoint;
		var d1 = this.spanA;
		var	d2 = this.spanB;
		var bp = this.positionVector;
		var  a = sum(d1**2);
		var  b = (d1<|> d2);
		var  d = b;
		var  e = sum(d2**2);
		var  c = ((aPoint-bp) <|> d1);
		var  f =  ((aPoint-bp) <|> d2);
		var delta = (a*e)-(b*d) + 0.0;
		var alpha = ((c*e)-(b*f)) / delta;
		var beta = ((a*f)-(c*d))/delta;
		^[alpha,beta]
	}

	projectionPoint2Plane{arg aPoint;
		var alpha,beta;
		#alpha,beta=this.prProjectionScalars(aPoint);
		^(this.positionVector + (alpha * this.spanA) + (beta * this.spanB));
	}

	//TODO
	//isCrossing{arg aLine;}
	//isParallel{arg aPlane;}
	//isOrthogonal{arg aLine;}
	//crossingPoint{arg aLine;}//returns a positionVector;
	//crossingLine{arg aPlane;}//returns a LineND
}