X-Git-Url: http://shamusworld.gotdns.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=src%2Fvector.cpp;h=89b9148a44343b6aa7f3c00bbf8210099731f97f;hb=5d8c9e52606315fbfe857f2715b8f051b4f97491;hp=da0d4c557aae2fe4e68b5df17d8cf0d4ce5f0ccf;hpb=9f6ad3fe0b9cb30115a5d38e8af3aebed0d70c08;p=architektonas diff --git a/src/vector.cpp b/src/vector.cpp index da0d4c5..89b9148 100644 --- a/src/vector.cpp +++ b/src/vector.cpp @@ -1,171 +1,275 @@ -// -// vector.cpp: Various structures used for 3 dimensional imaging -// -// by James L. Hammons -// (C) 2006 Underground Software -// -// JLH = James L. Hammons -// -// WHO WHEN WHAT -// --- ---------- ------------------------------------------------------------ -// JLH 09/19/2006 Created this file -// JLH 03/22/2011 Moved implementation of constructor from header to here -// JLH 04/02/2011 Fixed divide-by-zero bug in Unit(), added Angle() function -// - -#include "vector.h" - -#include // For sqrt() -#include "mathconstants.h" - - -// Vector implementation - -Vector::Vector(double xx/*= 0*/, double yy/*= 0*/, double zz/*= 0*/): x(xx), y(yy), z(zz) -{ -} - -Vector Vector::operator=(Vector const v) -{ - x = v.x, y = v.y, z = v.z; - - return *this; -} - -Vector Vector::operator+(Vector const v) -{ - return Vector(x + v.x, y + v.y, z + v.z); -} - -Vector Vector::operator-(Vector const v) -{ - return Vector(x - v.x, y - v.y, z - v.z); -} - -// Unary negation - -Vector Vector::operator-(void) -{ - return Vector(-x, -y, -z); -} - -// Vector x constant - -Vector Vector::operator*(double const v) -{ - return Vector(x * v, y * v, z * v); -} - -// Vector x constant - -Vector Vector::operator*(float const v) -{ - return Vector(x * v, y * v, z * v); -} - -// Vector / constant - -Vector Vector::operator/(double const v) -{ - return Vector(x / v, y / v, z / v); -} - -// Vector / constant - -Vector Vector::operator/(float const v) -{ - return Vector(x / v, y / v, z / v); -} - -// Vector (cross) product - -Vector Vector::operator*(Vector const v) -{ - // a x b = [a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1] - return Vector((y * v.z) - (z * v.y), (z * v.x) - (x * v.z), (x * v.y) - (y * v.x)); -} - -// Dot product - -double Vector::Dot(Vector const v) -{ - return (x * v.x) + (y * v.y) + (z * v.z); -} - - -// Vector x constant, self assigned - -Vector& Vector::operator*=(double const v) -{ - x *= v, y *= v, z *= v; - - return *this; -} - -// Vector / constant, self assigned - -Vector& Vector::operator/=(double const v) -{ - x /= v, y /= v, z /= v; - - return *this; -} - -// Vector + vector, self assigned - -Vector& Vector::operator+=(Vector const v) -{ - x += v.x, y += v.y, z += v.z; - - return *this; -} - -// Vector + constant, self assigned - -Vector& Vector::operator+=(double const v) -{ - x += v, y += v, z += v; - - return *this; -} - - -Vector Vector::Unit(void) -{ - double mag = Magnitude(); - - // If the magnitude of the vector is zero, then the Unit vector is undefined... - if (mag == 0) - return Vector(0, 0, 0); - - return Vector(x / mag, y / mag, z / mag); -} - -double Vector::Magnitude(void) -{ - return sqrt(x * x + y * y + z * z); -} - -double Vector::Angle(void) -{ - // acos returns a value between zero and PI, which means we don't know which - // quadrant the angle is in... Though, if the y-coordinate of the vector is - // negative, that means that the angle is in quadrants III - IV. - double rawAngle = acos(Unit().x); - double correctedAngle = (y < 0 ? (2.0 * PI) - rawAngle : rawAngle); - - return correctedAngle; -} - -bool Vector::isZero(double epsilon/*= 1e-6*/) -{ - return (fabs(x) < epsilon && fabs(y) < epsilon && fabs(z) < epsilon ? true : false); -} - - -// Class methods - -double Vector::Dot(Vector v1, Vector v2) -{ - return (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z); -} +// +// vector.cpp: Various structures used for 3 dimensional imaging +// +// by James Hammons +// (C) 2006 Underground Software +// +// JLH = James L. Hammons +// +// WHO WHEN WHAT +// --- ---------- ------------------------------------------------------------ +// JLH 09/19/2006 Created this file +// JLH 03/22/2011 Moved implementation of constructor from header to here +// JLH 04/02/2011 Fixed divide-by-zero bug in Unit(), added Angle() function +// JLH 08/04/2013 Added Parameter() function +// + +#include "vector.h" + +#include // For sqrt() +#include "mathconstants.h" + +// Vector implementation + +Vector::Vector(double xx/*= 0*/, double yy/*= 0*/, double zz/*= 0*/): x(xx), y(yy), z(zz) +{ +} + +Vector::Vector(Vector tail, Vector head): x(head.x - tail.x), y(head.y - tail.y), z(head.z - tail.z) +{ +} + +Vector::Vector(const Vector &v): x(v.x), y(v.y), z(v.z) +{ +} + +// Create vector from angle + length (2D; z is set to zero) +void Vector::SetAngleAndLength(double angle, double length) +{ + x = cos(angle) * length; + y = sin(angle) * length; + z = 0; +} + +Vector Vector::operator=(Vector const v) +{ + x = v.x, y = v.y, z = v.z; + + return *this; +} + +Vector Vector::operator+(Vector const v) +{ + return Vector(x + v.x, y + v.y, z + v.z); +} + +Vector Vector::operator-(Vector const v) +{ + return Vector(x - v.x, y - v.y, z - v.z); +} + +// Unary negation + +Vector Vector::operator-(void) +{ + return Vector(-x, -y, -z); +} + +// Vector x constant + +Vector Vector::operator*(double const v) +{ + return Vector(x * v, y * v, z * v); +} + +// Vector x constant + +Vector Vector::operator*(float const v) +{ + return Vector(x * v, y * v, z * v); +} + +// Vector / constant + +Vector Vector::operator/(double const v) +{ + return Vector(x / v, y / v, z / v); +} + +// Vector / constant + +Vector Vector::operator/(float const v) +{ + return Vector(x / v, y / v, z / v); +} + +// Vector (cross) product + +Vector Vector::operator*(Vector const v) +{ + // a x b = [a2b3 - a3b2, a3b1 - a1b3, a1b2 - a2b1] + return Vector((y * v.z) - (z * v.y), (z * v.x) - (x * v.z), (x * v.y) - (y * v.x)); +} + +// Dot product + +double Vector::Dot(Vector const v) +{ + return (x * v.x) + (y * v.y) + (z * v.z); +} + +// Vector x constant, self assigned + +Vector& Vector::operator*=(double const v) +{ + x *= v, y *= v, z *= v; + + return *this; +} + +// Vector / constant, self assigned + +Vector& Vector::operator/=(double const v) +{ + x /= v, y /= v, z /= v; + + return *this; +} + +// Vector + vector, self assigned + +Vector& Vector::operator+=(Vector const v) +{ + x += v.x, y += v.y, z += v.z; + + return *this; +} + +// Vector + constant, self assigned + +Vector& Vector::operator+=(double const v) +{ + x += v, y += v, z += v; + + return *this; +} + +// Vector - vector, self assigned + +Vector& Vector::operator-=(Vector const v) +{ + x -= v.x, y -= v.y, z -= v.z; + + return *this; +} + +// Vector - constant, self assigned + +Vector& Vector::operator-=(double const v) +{ + x -= v, y -= v, z -= v; + + return *this; +} + +// Check for equality +bool Vector::operator==(Vector const v) +{ + return (x == v.x && y == v.y && z == v.z ? true : false); +} + +// Check for inequality +bool Vector::operator!=(Vector const v) +{ + return (x != v.x || y != v.y || z != v.z ? true : false); +} + +Vector Vector::Unit(void) +{ + double mag = Magnitude(); + + // If the magnitude of the vector is zero, then the Unit vector is + // undefined... + if (mag == 0) + return Vector(0, 0, 0); + + return Vector(x / mag, y / mag, z / mag); +} + +double Vector::Magnitude(void) +{ + return sqrt((x * x) + (y * y) + (z * z)); +} + +double Vector::Angle(void) +{ + // acos returns a value between zero and TAU/2, which means we don't know + // which quadrant the angle is in... However, if the y-coordinate of the + // vector is negative, that means that the angle is in quadrants III - IV. + double rawAngle = acos(Unit().x); + double correctedAngle = (y < 0 ? TAU - rawAngle : rawAngle); + + return correctedAngle; +} + +bool Vector::isZero(double epsilon/*= 1e-6*/) +{ + return (fabs(x) < epsilon && fabs(y) < epsilon && fabs(z) < epsilon ? true : false); +} + +// Class methods + +/*static*/ double Vector::Dot(Vector v1, Vector v2) +{ + return (v1.x * v2.x) + (v1.y * v2.y) + (v1.z * v2.z); +} + +/*static*/ double Vector::Magnitude(Vector v1, Vector v2) +{ + double xx = v1.x - v2.x; + double yy = v1.y - v2.y; + double zz = v1.z - v2.z; + + return sqrt((xx * xx) + (yy * yy) + (zz * zz)); +} + +// +// Convenience function +// +/*static*/ double Vector::Angle(Point p1, Point p2) +{ + return Vector(p1, p2).Angle(); +} + +// Returns the parameter of a point in space to this vector. If the parameter +// is between 0 and 1, the normal of the vector to the point is on the vector. +// Note: v1 is the tail, v2 is the head of the line (vector). +/*static*/ double Vector::Parameter(Vector tail, Vector head, Vector p) +{ + // Geometric interpretation: + // The parameterized point on the vector lineSegment is where the normal of + // the lineSegment to the point intersects lineSegment. If the pp < 0, then + // the perpendicular lies beyond the 1st endpoint. If pp > 1, then the + // perpendicular lies beyond the 2nd endpoint. + + Vector lineSegment = head - tail; + double magnitude = lineSegment.Magnitude(); + Vector pointSegment = p - tail; + double t = lineSegment.Dot(pointSegment) / (magnitude * magnitude); + + return t; +} + +// Return the 2D normal to the linesegment formed by the passed in points. +// The normal thus calculated should rotate anti-clockwise. +/*static*/ Vector Vector::Normal(Vector tail, Vector head) +{ + Vector v = (head - tail).Unit(); + + return Vector(-v.y, v.x); +} + +/*static*/ double Vector::AngleBetween(Vector a, Vector b) +{ + // This is done using the following formula: + // (a . b) = ||a|| ||b|| cos(theta) + // However, have to check for two degenerate cases, where a = cb: + // 1) if c > 0, theta = 0; 2) if c < 0, theta = 180°. + // Also, the vectors a & b have to be non-zero. + // Also, have to check using an epsilon because acos will not return an + // exact value if the vectors are orthogonal. + if (a.isZero() || b.isZero()) + return 0; + + return acos(a.Dot(b) / (a.Magnitude() * b.Magnitude())); +}