Starting Eigen 2 development. The current plan is to use the last

release of tvmet (inactive for 2 years and developer unreachable) as the
basis for eigen2, because it provides seemingly good expression template
mechanisms, we want that, and it would take years to reinvent that
wheel. We'll see. So this commit imports the last tvmet release.

tvmet-1.7.1/examples/ray.cc

@@ -0,0 +1,103 @@
+#include <iostream>
+#include <cmath>
+
+#include <tvmet/Vector.h>
+
+using namespace std;
+using namespace tvmet;
+
+typedef Vector<double,3>	vector3d;
+
+void reflect(vector3d& reflection, const vector3d& ray, const vector3d& surfaceNormal)
+{
+  // The surface normal must be unit length to use this equation.
+  reflection = ray - 2 * dot(ray,surfaceNormal) * surfaceNormal;
+
+  // expression printing
+  //  cout << (ray - 2 * dot(ray,surfaceNormal) * surfaceNormal) << endl;
+}
+
+int main()
+{
+  vector3d x, y, z;
+
+  // y will be the incident ray
+  y[0] = 1;
+  y[1] = 0;
+  y[2] = -1;
+
+  // z is the surface normal
+  z[0] = 0;
+  z[1] = 0;
+  z[2] = 1;
+
+  reflect(x, y, z);
+
+  cout << "Reflected ray is: [ " << x[0] << " " << x[1] << " " << x[2]
+       << " ]" << endl;
+}
+
+/*****************************************************************************************
+gcc 3.2.0 produce this code (i586) using tvmet 1.3.0:
+
+_Z7reflectRN5tvmet6VectorIdLj3EEERKS1_S4_:
+.LFB2757:
+.L8:
+.L18:
+.L22:
+.L28:
+.L32:
+.L38:
+.L44:
+.L48:
+	pushl	%ebp
+.LCFI0:
+	movl	%esp, %ebp
+.LCFI1:
+	leal	-32(%ebp), %eax
+	pushl	%ebx
+.LCFI2:
+	subl	$52, %esp
+.LCFI3:
+	movl	16(%ebp), %edx
+	movl	%eax, -24(%ebp)
+	movl	12(%ebp), %ecx
+	leal	-36(%ebp), %eax
+	movl	%eax, -20(%ebp)
+	movl	8(%ebp), %ebx
+	leal	-24(%ebp), %eax
+	fldl	8(%edx)
+	fldl	16(%edx)
+	fmull	16(%ecx)
+	fxch	%st(1)
+	movl	%eax, -12(%ebp)
+	leal	-52(%ebp), %eax
+	fmull	8(%ecx)
+	movl	%eax, -48(%ebp)
+	leal	-12(%ebp), %eax
+	fldl	(%edx)
+	fmull	(%ecx)
+	fxch	%st(1)
+	movl	%eax, -44(%ebp)
+	faddp	%st, %st(2)
+	faddp	%st, %st(1)
+	fadd	%st(0), %st
+	fld	%st(0)
+	fstl	-32(%ebp)
+	fxch	%st(1)
+	fmull	(%edx)
+	fsubrl	(%ecx)
+	fstpl	(%ebx)
+	fld	%st(0)
+	fmull	8(%edx)
+	fsubrl	8(%ecx)
+	fstpl	8(%ebx)
+	fmull	16(%edx)
+	fsubrl	16(%ecx)
+	fstpl	16(%ebx)
+	addl	$52, %esp
+	popl	%ebx
+	popl	%ebp
+	ret
+
+*****************************************************************************************/