RayTracing

1. Matrix

   • Matrix
   • Matrix
   • SCALAR / SCALAR
   • Matrix mod ~ transpose // ! inverse // // adjoint // print

2. Vector

   • Vector
   • Vector
   • Scalar / Scalar ^ Vector dot
   • Vector cross unit mod mod2 transform Matrix<3> transform Matrix<4> // rotate // Vector component reflect

3. Color

4. Point

5. Ray

/*

Trace(ray){ p = infinity tri = null; For every triangle t{ i = intersection of ray and t if(i is inside t and on ray){ if(p.z > i.z){ p = i; tri = t; } } }

ray.color = p.color;

if(p != infinity){
	reflectedRay = ray.reflect(normal of tri at p)
	Trace(reflecedRay);
	ray.color = reflectedRay.color/10 + ray.color*9/10
}

}

Ray.Intersect(Surface){

int mFactor = 1;
int dFactor = 1;
int limit = 1000; // 0.001 - 3 decimal places

int mFUL = -1;

while(dFactor != 1000){
	i = Sruface(Ray);
	if(i > 0){
		if(mFactor != mFUL) mFactor *= 10;
		Ray.v += Ray.dir.unit() * (mFactor/dFactor);
	}else if(i < 0){
		if(mFUL == -1){
			mFUL = mFactor/10;
		}
		if(mFactor > 1){
			mFactor /= 10;
		}else{
			dFactor *= 10;
		}
	}else{
		return;
	}		
}
return;

}

Consider points in 3d. Assumption: they lie on poly curve

Xn Xn-1 Xn-2 . . .. . X0 (n+1 terms) Yn ... Zn ...

no of terms in expansion of (X + Y + Z + 1)^n

(x1 y1 z1 1)(x2 y2 z2 1) ... (xn yn zn 1)k = 3n + 1 independent terms

3n + 1 > number of points on object

3n + 1 > k

n > (k-1)/3

*/