343 lines
12 KiB
C
343 lines
12 KiB
C
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// Copyright (C) 2002-2012 Nikolaus Gebhardt
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// This file is part of the "Irrlicht Engine".
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// For conditions of distribution and use, see copyright notice in irrlicht.h
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#ifndef __IRR_POINT_2D_H_INCLUDED__
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#define __IRR_POINT_2D_H_INCLUDED__
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#include "irrMath.h"
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#include "dimension2d.h"
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namespace irr
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{
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namespace core
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{
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//! 2d vector template class with lots of operators and methods.
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/** As of Irrlicht 1.6, this class supercedes position2d, which should
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be considered deprecated. */
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template <class T>
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class vector2d
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{
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public:
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//! Default constructor (null vector)
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vector2d() : X(0), Y(0) {}
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//! Constructor with two different values
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vector2d(T nx, T ny) : X(nx), Y(ny) {}
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//! Constructor with the same value for both members
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explicit vector2d(T n) : X(n), Y(n) {}
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//! Copy constructor
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vector2d(const vector2d<T>& other) : X(other.X), Y(other.Y) {}
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vector2d(const dimension2d<T>& other) : X(other.Width), Y(other.Height) {}
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// operators
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vector2d<T> operator-() const { return vector2d<T>(-X, -Y); }
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vector2d<T>& operator=(const vector2d<T>& other) { X = other.X; Y = other.Y; return *this; }
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vector2d<T>& operator=(const dimension2d<T>& other) { X = other.Width; Y = other.Height; return *this; }
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vector2d<T> operator+(const vector2d<T>& other) const { return vector2d<T>(X + other.X, Y + other.Y); }
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vector2d<T> operator+(const dimension2d<T>& other) const { return vector2d<T>(X + other.Width, Y + other.Height); }
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vector2d<T>& operator+=(const vector2d<T>& other) { X+=other.X; Y+=other.Y; return *this; }
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vector2d<T> operator+(const T v) const { return vector2d<T>(X + v, Y + v); }
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vector2d<T>& operator+=(const T v) { X+=v; Y+=v; return *this; }
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vector2d<T>& operator+=(const dimension2d<T>& other) { X += other.Width; Y += other.Height; return *this; }
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vector2d<T> operator-(const vector2d<T>& other) const { return vector2d<T>(X - other.X, Y - other.Y); }
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vector2d<T> operator-(const dimension2d<T>& other) const { return vector2d<T>(X - other.Width, Y - other.Height); }
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vector2d<T>& operator-=(const vector2d<T>& other) { X-=other.X; Y-=other.Y; return *this; }
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vector2d<T> operator-(const T v) const { return vector2d<T>(X - v, Y - v); }
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vector2d<T>& operator-=(const T v) { X-=v; Y-=v; return *this; }
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vector2d<T>& operator-=(const dimension2d<T>& other) { X -= other.Width; Y -= other.Height; return *this; }
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vector2d<T> operator*(const vector2d<T>& other) const { return vector2d<T>(X * other.X, Y * other.Y); }
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vector2d<T>& operator*=(const vector2d<T>& other) { X*=other.X; Y*=other.Y; return *this; }
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vector2d<T> operator*(const T v) const { return vector2d<T>(X * v, Y * v); }
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vector2d<T>& operator*=(const T v) { X*=v; Y*=v; return *this; }
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vector2d<T> operator/(const vector2d<T>& other) const { return vector2d<T>(X / other.X, Y / other.Y); }
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vector2d<T>& operator/=(const vector2d<T>& other) { X/=other.X; Y/=other.Y; return *this; }
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vector2d<T> operator/(const T v) const { return vector2d<T>(X / v, Y / v); }
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vector2d<T>& operator/=(const T v) { X/=v; Y/=v; return *this; }
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//! sort in order X, Y. Equality with rounding tolerance.
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bool operator<=(const vector2d<T>&other) const
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{
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return (X<other.X || core::equals(X, other.X)) ||
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(core::equals(X, other.X) && (Y<other.Y || core::equals(Y, other.Y)));
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}
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//! sort in order X, Y. Equality with rounding tolerance.
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bool operator>=(const vector2d<T>&other) const
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{
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return (X>other.X || core::equals(X, other.X)) ||
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(core::equals(X, other.X) && (Y>other.Y || core::equals(Y, other.Y)));
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}
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//! sort in order X, Y. Difference must be above rounding tolerance.
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bool operator<(const vector2d<T>&other) const
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{
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return (X<other.X && !core::equals(X, other.X)) ||
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(core::equals(X, other.X) && Y<other.Y && !core::equals(Y, other.Y));
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}
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//! sort in order X, Y. Difference must be above rounding tolerance.
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bool operator>(const vector2d<T>&other) const
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{
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return (X>other.X && !core::equals(X, other.X)) ||
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(core::equals(X, other.X) && Y>other.Y && !core::equals(Y, other.Y));
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}
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bool operator==(const vector2d<T>& other) const { return equals(other); }
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bool operator!=(const vector2d<T>& other) const { return !equals(other); }
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// functions
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//! Checks if this vector equals the other one.
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/** Takes floating point rounding errors into account.
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\param other Vector to compare with.
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\return True if the two vector are (almost) equal, else false. */
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bool equals(const vector2d<T>& other) const
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{
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return core::equals(X, other.X) && core::equals(Y, other.Y);
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}
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vector2d<T>& set(T nx, T ny) {X=nx; Y=ny; return *this; }
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vector2d<T>& set(const vector2d<T>& p) { X=p.X; Y=p.Y; return *this; }
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//! Gets the length of the vector.
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/** \return The length of the vector. */
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T getLength() const { return core::squareroot( X*X + Y*Y ); }
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//! Get the squared length of this vector
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/** This is useful because it is much faster than getLength().
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\return The squared length of the vector. */
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T getLengthSQ() const { return X*X + Y*Y; }
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//! Get the dot product of this vector with another.
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/** \param other Other vector to take dot product with.
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\return The dot product of the two vectors. */
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T dotProduct(const vector2d<T>& other) const
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{
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return X*other.X + Y*other.Y;
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}
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//! Gets distance from another point.
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/** Here, the vector is interpreted as a point in 2-dimensional space.
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\param other Other vector to measure from.
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\return Distance from other point. */
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T getDistanceFrom(const vector2d<T>& other) const
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{
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return vector2d<T>(X - other.X, Y - other.Y).getLength();
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}
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//! Returns squared distance from another point.
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/** Here, the vector is interpreted as a point in 2-dimensional space.
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\param other Other vector to measure from.
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\return Squared distance from other point. */
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T getDistanceFromSQ(const vector2d<T>& other) const
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{
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return vector2d<T>(X - other.X, Y - other.Y).getLengthSQ();
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}
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//! rotates the point anticlockwise around a center by an amount of degrees.
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/** \param degrees Amount of degrees to rotate by, anticlockwise.
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\param center Rotation center.
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\return This vector after transformation. */
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vector2d<T>& rotateBy(f64 degrees, const vector2d<T>& center=vector2d<T>())
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{
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degrees *= DEGTORAD64;
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const f64 cs = cos(degrees);
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const f64 sn = sin(degrees);
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X -= center.X;
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Y -= center.Y;
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set((T)(X*cs - Y*sn), (T)(X*sn + Y*cs));
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X += center.X;
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Y += center.Y;
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return *this;
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}
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//! Normalize the vector.
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/** The null vector is left untouched.
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\return Reference to this vector, after normalization. */
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vector2d<T>& normalize()
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{
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f32 length = (f32)(X*X + Y*Y);
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if ( length == 0 )
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return *this;
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length = core::reciprocal_squareroot ( length );
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X = (T)(X * length);
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Y = (T)(Y * length);
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return *this;
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}
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//! Calculates the angle of this vector in degrees in the trigonometric sense.
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/** 0 is to the right (3 o'clock), values increase counter-clockwise.
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This method has been suggested by Pr3t3nd3r.
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\return Returns a value between 0 and 360. */
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f64 getAngleTrig() const
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{
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if (Y == 0)
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return X < 0 ? 180 : 0;
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else
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if (X == 0)
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return Y < 0 ? 270 : 90;
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if ( Y > 0)
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if (X > 0)
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return atan((irr::f64)Y/(irr::f64)X) * RADTODEG64;
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else
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return 180.0-atan((irr::f64)Y/-(irr::f64)X) * RADTODEG64;
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else
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if (X > 0)
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return 360.0-atan(-(irr::f64)Y/(irr::f64)X) * RADTODEG64;
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else
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return 180.0+atan(-(irr::f64)Y/-(irr::f64)X) * RADTODEG64;
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}
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//! Calculates the angle of this vector in degrees in the counter trigonometric sense.
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/** 0 is to the right (3 o'clock), values increase clockwise.
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\return Returns a value between 0 and 360. */
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inline f64 getAngle() const
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{
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if (Y == 0) // corrected thanks to a suggestion by Jox
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return X < 0 ? 180 : 0;
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else if (X == 0)
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return Y < 0 ? 90 : 270;
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// don't use getLength here to avoid precision loss with s32 vectors
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// avoid floating-point trouble as sqrt(y*y) is occasionally larger than y, so clamp
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const f64 tmp = core::clamp(Y / sqrt((f64)(X*X + Y*Y)), -1.0, 1.0);
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const f64 angle = atan( core::squareroot(1 - tmp*tmp) / tmp) * RADTODEG64;
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if (X>0 && Y>0)
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return angle + 270;
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else
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if (X>0 && Y<0)
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return angle + 90;
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else
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if (X<0 && Y<0)
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return 90 - angle;
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else
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if (X<0 && Y>0)
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return 270 - angle;
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return angle;
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}
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//! Calculates the angle between this vector and another one in degree.
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/** \param b Other vector to test with.
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\return Returns a value between 0 and 90. */
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inline f64 getAngleWith(const vector2d<T>& b) const
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{
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f64 tmp = (f64)(X*b.X + Y*b.Y);
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if (tmp == 0.0)
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return 90.0;
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tmp = tmp / core::squareroot((f64)((X*X + Y*Y) * (b.X*b.X + b.Y*b.Y)));
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if (tmp < 0.0)
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tmp = -tmp;
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if ( tmp > 1.0 ) // avoid floating-point trouble
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tmp = 1.0;
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return atan(sqrt(1 - tmp*tmp) / tmp) * RADTODEG64;
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}
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//! Returns if this vector interpreted as a point is on a line between two other points.
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/** It is assumed that the point is on the line.
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\param begin Beginning vector to compare between.
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\param end Ending vector to compare between.
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\return True if this vector is between begin and end, false if not. */
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bool isBetweenPoints(const vector2d<T>& begin, const vector2d<T>& end) const
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{
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if (begin.X != end.X)
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{
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return ((begin.X <= X && X <= end.X) ||
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(begin.X >= X && X >= end.X));
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}
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else
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{
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return ((begin.Y <= Y && Y <= end.Y) ||
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(begin.Y >= Y && Y >= end.Y));
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}
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}
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//! Creates an interpolated vector between this vector and another vector.
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/** \param other The other vector to interpolate with.
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\param d Interpolation value between 0.0f (all the other vector) and 1.0f (all this vector).
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Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
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\return An interpolated vector. This vector is not modified. */
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vector2d<T> getInterpolated(const vector2d<T>& other, f64 d) const
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{
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f64 inv = 1.0f - d;
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return vector2d<T>((T)(other.X*inv + X*d), (T)(other.Y*inv + Y*d));
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}
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//! Creates a quadratically interpolated vector between this and two other vectors.
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/** \param v2 Second vector to interpolate with.
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\param v3 Third vector to interpolate with (maximum at 1.0f)
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\param d Interpolation value between 0.0f (all this vector) and 1.0f (all the 3rd vector).
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Note that this is the opposite direction of interpolation to getInterpolated() and interpolate()
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\return An interpolated vector. This vector is not modified. */
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vector2d<T> getInterpolated_quadratic(const vector2d<T>& v2, const vector2d<T>& v3, f64 d) const
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{
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// this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
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const f64 inv = 1.0f - d;
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const f64 mul0 = inv * inv;
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const f64 mul1 = 2.0f * d * inv;
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const f64 mul2 = d * d;
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return vector2d<T> ( (T)(X * mul0 + v2.X * mul1 + v3.X * mul2),
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(T)(Y * mul0 + v2.Y * mul1 + v3.Y * mul2));
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}
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//! Sets this vector to the linearly interpolated vector between a and b.
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/** \param a first vector to interpolate with, maximum at 1.0f
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\param b second vector to interpolate with, maximum at 0.0f
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\param d Interpolation value between 0.0f (all vector b) and 1.0f (all vector a)
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Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
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*/
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vector2d<T>& interpolate(const vector2d<T>& a, const vector2d<T>& b, f64 d)
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{
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X = (T)((f64)b.X + ( ( a.X - b.X ) * d ));
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Y = (T)((f64)b.Y + ( ( a.Y - b.Y ) * d ));
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return *this;
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}
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//! X coordinate of vector.
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T X;
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//! Y coordinate of vector.
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T Y;
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};
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//! Typedef for f32 2d vector.
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typedef vector2d<f32> vector2df;
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//! Typedef for integer 2d vector.
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typedef vector2d<s32> vector2di;
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template<class S, class T>
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vector2d<T> operator*(const S scalar, const vector2d<T>& vector) { return vector*scalar; }
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// These methods are declared in dimension2d, but need definitions of vector2d
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template<class T>
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dimension2d<T>::dimension2d(const vector2d<T>& other) : Width(other.X), Height(other.Y) { }
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template<class T>
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bool dimension2d<T>::operator==(const vector2d<T>& other) const { return Width == other.X && Height == other.Y; }
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} // end namespace core
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} // end namespace irr
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#endif
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