Bart Janssens
Simple Vector Library 1.5 http://www.cs.cmu.edu/~ajw/doc/svl.html
Diff: Mat2.h
- Revision:
- 0:785cff1e5a7c
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/Mat2.h Mon Jan 04 15:19:10 2016 +0000
@@ -0,0 +1,381 @@
+/*
+ File: Mat2.h
+
+ Function: Defines a 2 x 2 matrix.
+
+ Author(s): Andrew Willmott
+
+ Copyright: (c) 1995-2001, Andrew Willmott
+ */
+
+#ifndef __Mat2__
+#define __Mat2__
+
+#include "Vec2.h"
+
+
+// --- Mat2 Class -------------------------------------------------------------
+
+class Mat2
+{
+public:
+
+ // Constructors
+
+ Mat2();
+ Mat2(Real a, Real b, Real c, Real d); // Create from rows
+ Mat2(const Mat2 &m); // Copy constructor
+ Mat2(ZeroOrOne k);
+ Mat2(Block k);
+
+ // Accessor functions
+
+ Int Rows() const { return(2); };
+ Int Cols() const { return(2); };
+
+ Vec2 &operator [] (Int i);
+ const Vec2 &operator [] (Int i) const;
+
+ Real *Ref() const; // Return pointer to data
+
+ // Assignment operators
+
+ Mat2 &operator = (const Mat2 &m);
+ Mat2 &operator = (ZeroOrOne k);
+ Mat2 &operator = (Block k);
+ Mat2 &operator += (const Mat2 &m);
+ Mat2 &operator -= (const Mat2 &m);
+ Mat2 &operator *= (const Mat2 &m);
+ Mat2 &operator *= (Real s);
+ Mat2 &operator /= (Real s);
+
+ // Comparison operators
+
+ Bool operator == (const Mat2 &m) const; // M == N?
+ Bool operator != (const Mat2 &m) const; // M != N?
+
+ // Arithmetic operators
+
+ Mat2 operator + (const Mat2 &m) const; // M + N
+ Mat2 operator - (const Mat2 &m) const; // M - N
+ Mat2 operator - () const; // -M
+ Mat2 operator * (const Mat2 &m) const; // M * N
+ Mat2 operator * (Real s) const; // M * s
+ Mat2 operator / (Real s) const; // M / s
+
+ // Initialisers
+
+ Void MakeZero(); // Zero matrix
+ Void MakeDiag(Real k = vl_one); // I
+ Void MakeBlock(Real k = vl_one); // all elts=k
+
+ // Vector Transformations
+
+ Mat2& MakeRot(Real theta);
+ Mat2& MakeScale(const Vec2 &s);
+
+ // Private...
+
+protected:
+
+ Vec2 row[2]; // Rows of the matrix
+};
+
+
+// --- Matrix operators -------------------------------------------------------
+
+inline Vec2 &operator *= (Vec2 &v, const Mat2 &m); // v *= m
+inline Vec2 operator * (const Mat2 &m, const Vec2 &v); // m * v
+inline Vec2 operator * (const Vec2 &v, const Mat2 &m); // v * m
+inline Mat2 operator * (Real s, const Mat2 &m); // s * m
+
+inline Mat2 trans(const Mat2 &m); // Transpose
+inline Real trace(const Mat2 &m); // Trace
+inline Mat2 adj(const Mat2 &m); // Adjoint
+Real det(const Mat2 &m); // Determinant
+Mat2 inv(const Mat2 &m); // Inverse
+Mat2 oprod(const Vec2 &a, const Vec2 &b);
+ // Outer product
+
+// The xform functions help avoid dependence on whether row or column
+// vectors are used to represent points and vectors.
+inline Vec2 xform(const Mat2 &m, const Vec2 &v); // Transform of v by m
+inline Mat2 xform(const Mat2 &m, const Mat2 &n); // xform v -> m(n(v))
+
+//std::ostream &operator << (std::ostream &s, const Mat2 &m);
+//std::istream &operator >> (std::istream &s, Mat2 &m);
+
+void printMat2(const Mat2 &m);
+
+
+// --- Inlines ----------------------------------------------------------------
+
+inline Vec2 &Mat2::operator [] (Int i)
+{
+ CheckRange(i, 0, 2, "(Mat2::[i]) index out of range");
+ return(row[i]);
+}
+
+inline const Vec2 &Mat2::operator [] (Int i) const
+{
+ CheckRange(i, 0, 2, "(Mat2::[i]) index out of range");
+ return(row[i]);
+}
+
+inline Real *Mat2::Ref() const
+{
+ return((Real*) row);
+}
+
+inline Mat2::Mat2()
+{
+}
+
+inline Mat2::Mat2(Real a, Real b, Real c, Real d)
+{
+ row[0][0] = a; row[0][1] = b;
+ row[1][0] = c; row[1][1] = d;
+}
+
+inline Mat2::Mat2(const Mat2 &m)
+{
+ row[0] = m[0];
+ row[1] = m[1];
+}
+
+
+inline Void Mat2::MakeZero()
+{
+ row[0][0] = vl_zero; row[0][1] = vl_zero;
+ row[1][0] = vl_zero; row[1][1] = vl_zero;
+}
+
+inline Void Mat2::MakeDiag(Real k)
+{
+ row[0][0] = k; row[0][1] = vl_zero;
+ row[1][0] = vl_zero; row[1][1] = k;
+}
+
+inline Void Mat2::MakeBlock(Real k)
+{
+ row[0][0] = k; row[0][1] = k;
+ row[1][0] = k; row[1][1] = k;
+}
+
+inline Mat2::Mat2(ZeroOrOne k)
+{
+ MakeDiag(k);
+}
+
+inline Mat2::Mat2(Block k)
+{
+ MakeBlock((ZeroOrOne) k);
+}
+
+inline Mat2 &Mat2::operator = (ZeroOrOne k)
+{
+ MakeDiag(k);
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator = (Block k)
+{
+ MakeBlock((ZeroOrOne) k);
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator = (const Mat2 &m)
+{
+ row[0] = m[0];
+ row[1] = m[1];
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator += (const Mat2 &m)
+{
+ row[0] += m[0];
+ row[1] += m[1];
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator -= (const Mat2 &m)
+{
+ row[0] -= m[0];
+ row[1] -= m[1];
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator *= (const Mat2 &m)
+{
+ SELF = SELF * m;
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator *= (Real s)
+{
+ row[0] *= s;
+ row[1] *= s;
+
+ return(SELF);
+}
+
+inline Mat2 &Mat2::operator /= (Real s)
+{
+ row[0] /= s;
+ row[1] /= s;
+
+ return(SELF);
+}
+
+
+inline Mat2 Mat2::operator + (const Mat2 &m) const
+{
+ Mat2 result;
+
+ result[0] = row[0] + m[0];
+ result[1] = row[1] + m[1];
+
+ return(result);
+}
+
+inline Mat2 Mat2::operator - (const Mat2 &m) const
+{
+ Mat2 result;
+
+ result[0] = row[0] - m[0];
+ result[1] = row[1] - m[1];
+
+ return(result);
+}
+
+inline Mat2 Mat2::operator - () const
+{
+ Mat2 result;
+
+ result[0] = -row[0];
+ result[1] = -row[1];
+
+ return(result);
+}
+
+inline Mat2 Mat2::operator * (const Mat2 &m) const
+{
+#define N(x,y) row[x][y]
+#define M(x,y) m.row[x][y]
+#define R(x,y) result[x][y]
+
+ Mat2 result;
+
+ R(0,0) = N(0,0) * M(0,0) + N(0,1) * M(1,0);
+ R(0,1) = N(0,0) * M(0,1) + N(0,1) * M(1,1);
+ R(1,0) = N(1,0) * M(0,0) + N(1,1) * M(1,0);
+ R(1,1) = N(1,0) * M(0,1) + N(1,1) * M(1,1);
+
+ return(result);
+
+#undef N
+#undef M
+#undef R
+}
+
+inline Mat2 Mat2::operator * (Real s) const
+{
+ Mat2 result;
+
+ result[0] = row[0] * s;
+ result[1] = row[1] * s;
+
+ return(result);
+}
+
+inline Mat2 Mat2::operator / (Real s) const
+{
+ Mat2 result;
+
+ result[0] = row[0] / s;
+ result[1] = row[1] / s;
+
+ return(result);
+}
+
+inline Mat2 operator * (Real s, const Mat2 &m)
+{
+ return(m * s);
+}
+
+inline Vec2 operator * (const Mat2 &m, const Vec2 &v)
+{
+ Vec2 result;
+
+ result[0] = m[0][0] * v[0] + m[0][1] * v[1];
+ result[1] = m[1][0] * v[0] + m[1][1] * v[1];
+
+ return(result);
+}
+
+inline Vec2 operator * (const Vec2 &v, const Mat2 &m)
+{
+ Vec2 result;
+
+ result[0] = v[0] * m[0][0] + v[1] * m[1][0];
+ result[1] = v[0] * m[0][1] + v[1] * m[1][1];
+
+ return(result);
+}
+
+inline Vec2 &operator *= (Vec2 &v, const Mat2 &m)
+{
+ Real t;
+
+ t = v[0] * m[0][0] + v[1] * m[1][0];
+ v[1] = v[0] * m[0][1] + v[1] * m[1][1];
+ v[0] = t;
+
+ return(v);
+}
+
+
+inline Mat2 trans(const Mat2 &m)
+{
+ Mat2 result;
+
+ result[0][0] = m[0][0]; result[0][1] = m[1][0];
+ result[1][0] = m[0][1]; result[1][1] = m[1][1];
+
+ return(result);
+}
+
+inline Real trace(const Mat2 &m)
+{
+ return(m[0][0] + m[1][1]);
+}
+
+inline Mat2 adj(const Mat2 &m)
+{
+ Mat2 result;
+
+ result[0] = cross(m[1]);
+ result[1] = -cross(m[0]);
+
+ return(result);
+}
+
+#ifdef VL_ROW_ORIENT
+inline Vec2 xform(const Mat2 &m, const Vec2 &v)
+{ return(v * m); }
+inline Mat2 xform(const Mat2 &m, const Mat2 &n)
+{ return(n * m); }
+#else
+inline Vec2 xform(const Mat2 &m, const Vec2 &v)
+{ return(m * v); }
+inline Mat2 xform(const Mat2 &m, const Mat2 &n)
+{ return(m * n); }
+#endif
+
+#endif