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libs/Common/Sphere.inl

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+////////////////////////////////////////////////////////////////////
+// Sphere.inl
+//
+// Copyright 2007 cDc@seacave
+// Distributed under the Boost Software License, Version 1.0
+// (See http://www.boost.org/LICENSE_1_0.txt)
+
+
+// D E F I N E S ///////////////////////////////////////////////////
+
+
+// S T R U C T S ///////////////////////////////////////////////////
+
+template <typename TYPE, int DIMS>
+inline TSphere<TYPE,DIMS>::TSphere(const POINT& p1, const POINT& p2, const POINT& p3)
+{
+	Set(p1, p2, p3);
+} // constructor
+/*----------------------------------------------------------------*/
+
+
+template <typename TYPE, int DIMS>
+inline void TSphere<TYPE,DIMS>::Set(const POINT& c, TYPE r)
+{
+	center = c;
+	radius = r;
+}
+template <typename TYPE, int DIMS>
+inline void TSphere<TYPE, DIMS>::Set(const POINT& p1, const POINT& p2, const POINT& p3)
+{
+	// compute relative distances
+	TYPE A((p1 - p2).squaredNorm());
+	TYPE B((p2 - p3).squaredNorm());
+	TYPE C((p3 - p1).squaredNorm());
+
+	// re-orient triangle (make A longest side)
+	const POINT *a(&p3), *b(&p1), *c(&p2);
+	if (B < C) std::swap(B, C), std::swap(b, c);
+	if (A < B) std::swap(A, B), std::swap(a, b);
+
+	// if obtuse
+	if (B + C <= A) {
+		// just use longest diameter
+		radius = SQRT(A) / TYPE(2);
+		center = (*b + *c) / TYPE(2);
+	} else {
+		// otherwise circumscribe (http://en.wikipedia.org/wiki/Circumscribed_circle)
+		const TYPE cos_a(SQUARE(B + C - A) / (B*C*TYPE(4)));
+		radius = SQRT(A / ((TYPE(1) - cos_a)*TYPE(4)));
+		const POINT alpha(*a - *c), beta(*b - *c);
+		const POINT alphaXbeta(alpha.cross(beta));
+		center = (beta * alpha.squaredNorm() - alpha * beta.squaredNorm()).cross(alphaXbeta) /
+			(alphaXbeta.squaredNorm() * TYPE(2)) + *c;
+	}
+}
+/*----------------------------------------------------------------*/
+
+
+template <typename TYPE, int DIMS>
+inline void TSphere<TYPE,DIMS>::Enlarge(TYPE x)
+{
+	radius += x;
+}
+template <typename TYPE, int DIMS>
+inline void TSphere<TYPE,DIMS>::EnlargePercent(TYPE x)
+{
+	radius *= x;
+} // Enlarge
+/*----------------------------------------------------------------*/
+
+
+// Classify point to sphere.
+template <typename TYPE, int DIMS>
+inline GCLASS TSphere<TYPE, DIMS>::Classify(const POINT& p) const
+{
+	if ((center - p).squaredNorm() > SQUARE(radius))
+		return CULLED;
+	return VISIBLE;
+}
+/*----------------------------------------------------------------*/