//\r
// vector.cpp: Various structures used for 3 dimensional imaging\r
//\r
-// by James L. Hammons\r
+// by James Hammons\r
// (C) 2006 Underground Software\r
//\r
// JLH = James L. Hammons <jlhamm@acm.org>\r
// JLH 09/19/2006 Created this file\r
// JLH 03/22/2011 Moved implementation of constructor from header to here\r
// JLH 04/02/2011 Fixed divide-by-zero bug in Unit(), added Angle() function\r
+// JLH 08/04/2013 Added Parameter() function\r
//\r
\r
#include "vector.h"\r
#include <math.h> // For sqrt()\r
#include "mathconstants.h"\r
\r
-\r
// Vector implementation\r
\r
Vector::Vector(double xx/*= 0*/, double yy/*= 0*/, double zz/*= 0*/): x(xx), y(yy), z(zz)\r
{\r
}\r
\r
+\r
Vector::Vector(Vector head, Vector tail): x(head.x - tail.x), y(head.y - tail.y), z(head.z - tail.z)\r
{\r
}\r
\r
+\r
Vector Vector::operator=(Vector const v)\r
{\r
x = v.x, y = v.y, z = v.z;\r
return *this;\r
}\r
\r
+\r
Vector Vector::operator+(Vector const v)\r
{\r
return Vector(x + v.x, y + v.y, z + v.z);\r
}\r
\r
+\r
Vector Vector::operator-(Vector const v)\r
{\r
return Vector(x - v.x, y - v.y, z - v.z);\r
}\r
\r
+\r
// Unary negation\r
\r
Vector Vector::operator-(void)\r
return Vector(-x, -y, -z);\r
}\r
\r
+\r
// Vector x constant\r
\r
Vector Vector::operator*(double const v)\r
return Vector(x * v, y * v, z * v);\r
}\r
\r
+\r
// Vector x constant\r
\r
Vector Vector::operator*(float const v)\r
return Vector(x * v, y * v, z * v);\r
}\r
\r
+\r
// Vector / constant\r
\r
Vector Vector::operator/(double const v)\r
return Vector(x / v, y / v, z / v);\r
}\r
\r
+\r
// Vector / constant\r
\r
Vector Vector::operator/(float const v)\r
return Vector(x / v, y / v, z / v);\r
}\r
\r
+\r
// Vector (cross) product\r
\r
Vector Vector::operator*(Vector const v)\r
return Vector((y * v.z) - (z * v.y), (z * v.x) - (x * v.z), (x * v.y) - (y * v.x));\r
}\r
\r
+\r
// Dot product\r
\r
double Vector::Dot(Vector const v)\r
return *this;\r
}\r
\r
+\r
// Vector / constant, self assigned\r
\r
Vector& Vector::operator/=(double const v)\r
return *this;\r
}\r
\r
+\r
// Vector + constant, self assigned\r
\r
Vector& Vector::operator+=(double const v)\r
return *this;\r
}\r
\r
+\r
// Vector - vector, self assigned\r
\r
Vector& Vector::operator-=(Vector const v)\r
return *this;\r
}\r
\r
+\r
// Vector - constant, self assigned\r
\r
Vector& Vector::operator-=(double const v)\r
}\r
\r
\r
+// Check for equality\r
+bool Vector::operator==(Vector const v)\r
+{\r
+ return (x == v.x && y == v.y && z == v.z ? true : false);\r
+}\r
+\r
+\r
+// Check for inequality\r
+bool Vector::operator!=(Vector const v)\r
+{\r
+ return (x != v.x || y != v.y || z != v.z ? true : false);\r
+}\r
+\r
+\r
Vector Vector::Unit(void)\r
{\r
double mag = Magnitude();\r
return Vector(x / mag, y / mag, z / mag);\r
}\r
\r
+\r
double Vector::Magnitude(void)\r
{\r
return sqrt(x * x + y * y + z * z);\r
}\r
\r
+\r
double Vector::Angle(void)\r
{\r
// acos returns a value between zero and PI, which means we don't know which\r
return correctedAngle;\r
}\r
\r
+\r
bool Vector::isZero(double epsilon/*= 1e-6*/)\r
{\r
return (fabs(x) < epsilon && fabs(y) < epsilon && fabs(z) < epsilon ? true : false);\r
return (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z);\r
}\r
\r
+\r
double Vector::Magnitude(Vector v1, Vector v2)\r
{\r
double xx = v1.x - v2.x;\r
double zz = v1.z - v2.z;\r
return sqrt(xx * xx + yy * yy + zz * zz);\r
}\r
+\r
+\r
+// Returns the parameter of a point in space to this vector. If the parameter\r
+// is between 0 and 1, the normal of the vector to the point is on the vector.\r
+double Vector::Parameter(Vector v1, Vector v2, Vector p)\r
+{\r
+ // Geometric interpretation:\r
+ // The parameterized point on the vector lineSegment is where the normal of\r
+ // the lineSegment to the point intersects lineSegment. If the pp < 0, then\r
+ // the perpendicular lies beyond the 1st endpoint. If pp > 1, then the\r
+ // perpendicular lies beyond the 2nd endpoint.\r
+\r
+ Vector lineSegment = v1 - v2;\r
+ double magnitude = lineSegment.Magnitude();\r
+ Vector pointSegment = p - v2;\r
+ double t = lineSegment.Dot(pointSegment) / (magnitude * magnitude);\r
+ return t;\r
+}\r
+\r
+\r
+// Return the normal to the linesegment formed by the passed in points.\r
+// (Not sure which is head or tail, or which hand the normal lies)\r
+/*static*/ Vector Vector::Normal(Vector v1, Vector v2)\r
+{\r
+ Vector v = (v1 - v2).Unit();\r
+ return Vector(-v.y, v.x);\r
+}\r
+\r