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504 lines
14 KiB
C
504 lines
14 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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#pragma once
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#include "irrMath.h"
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#include "dimension2d.h"
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#include <functional>
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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 supersedes 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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constexpr vector2d() :
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X(0), Y(0) {}
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//! Constructor with two different values
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constexpr vector2d(T nx, T ny) :
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X(nx), Y(ny) {}
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//! Constructor with the same value for both members
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explicit constexpr vector2d(T n) :
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X(n), Y(n) {}
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constexpr vector2d(const dimension2d<T> &other) :
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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 dimension2d<T> &other)
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{
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X = other.Width;
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Y = other.Height;
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return *this;
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}
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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)
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{
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X += other.X;
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Y += other.Y;
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return *this;
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}
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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)
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{
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X += v;
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Y += v;
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return *this;
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}
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vector2d<T> &operator+=(const dimension2d<T> &other)
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{
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X += other.Width;
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Y += other.Height;
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return *this;
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}
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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)
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{
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X -= other.X;
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Y -= other.Y;
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return *this;
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}
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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)
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{
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X -= v;
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Y -= v;
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return *this;
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}
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vector2d<T> &operator-=(const dimension2d<T> &other)
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{
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X -= other.Width;
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Y -= other.Height;
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return *this;
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}
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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)
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{
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X *= other.X;
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Y *= other.Y;
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return *this;
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}
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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)
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{
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X *= v;
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Y *= v;
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return *this;
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}
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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)
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{
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X /= other.X;
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Y /= other.Y;
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return *this;
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}
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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)
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{
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X /= v;
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Y /= v;
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return *this;
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}
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T &operator[](u32 index)
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{
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_IRR_DEBUG_BREAK_IF(index > 1) // access violation
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return *(&X + index);
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}
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const T &operator[](u32 index) const
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{
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_IRR_DEBUG_BREAK_IF(index > 1) // access violation
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return *(&X + index);
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}
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//! sort in order X, Y.
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constexpr bool operator<=(const vector2d<T> &other) const
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{
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return !(*this > other);
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}
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//! sort in order X, Y.
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constexpr bool operator>=(const vector2d<T> &other) const
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{
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return !(*this < other);
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}
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//! sort in order X, Y.
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constexpr bool operator<(const vector2d<T> &other) const
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{
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return X < other.X || (X == other.X && Y < other.Y);
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}
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//! sort in order X, Y.
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constexpr bool operator>(const vector2d<T> &other) const
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{
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return X > other.X || (X == other.X && Y > other.Y);
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}
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constexpr bool operator==(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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constexpr bool operator!=(const vector2d<T> &other) const
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{
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return !(*this == other);
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}
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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)
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{
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X = nx;
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Y = ny;
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return *this;
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}
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vector2d<T> &set(const vector2d<T> &p)
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{
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X = p.X;
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Y = p.Y;
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return *this;
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}
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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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//! check if this vector is parallel to another vector
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bool nearlyParallel(const vector2d<T> &other, const T factor = relativeErrorFactor<T>()) const
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{
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// https://eagergames.wordpress.com/2017/04/01/fast-parallel-lines-and-vectors-test/
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// if a || b then a.x/a.y = b.x/b.y (similar triangles)
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// if a || b then either both x are 0 or both y are 0.
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return equalsRelative(X * other.Y, other.X * Y, factor) && // a bit counterintuitive, but makes sure that
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// only y or only x are 0, and at same time deals
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// with the case where one vector is zero vector.
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(X * other.X + Y * other.Y) != 0;
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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> ¢er = 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 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 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 if (X > 0 && Y < 0)
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return angle + 90;
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else if (X < 0 && Y < 0)
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return 90 - angle;
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else 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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// . end
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// /
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// /
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// /
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// . begin
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// -
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// -
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// . this point (am I inside or outside)?
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//
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if (begin.X != end.X) {
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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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} else {
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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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const 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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/*! Test if this point and another 2 points taken as triplet
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are colinear, clockwise, anticlockwise. This can be used also
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to check winding order in triangles for 2D meshes.
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\return 0 if points are colinear, 1 if clockwise, 2 if anticlockwise
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*/
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s32 checkOrientation(const vector2d<T> &b, const vector2d<T> &c) const
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{
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// Example of clockwise points
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//
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// ^ Y
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// | A
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// | . .
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// | . .
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// | C.....B
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// +---------------> X
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T val = (b.Y - Y) * (c.X - b.X) -
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||
|
(b.X - X) * (c.Y - b.Y);
|
||
|
|
||
|
if (val == 0)
|
||
|
return 0; // colinear
|
||
|
|
||
|
return (val > 0) ? 1 : 2; // clock or counterclock wise
|
||
|
}
|
||
|
|
||
|
/*! Returns true if points (a,b,c) are clockwise on the X,Y plane*/
|
||
|
inline bool areClockwise(const vector2d<T> &b, const vector2d<T> &c) const
|
||
|
{
|
||
|
T val = (b.Y - Y) * (c.X - b.X) -
|
||
|
(b.X - X) * (c.Y - b.Y);
|
||
|
|
||
|
return val > 0;
|
||
|
}
|
||
|
|
||
|
/*! Returns true if points (a,b,c) are counterclockwise on the X,Y plane*/
|
||
|
inline bool areCounterClockwise(const vector2d<T> &b, const vector2d<T> &c) const
|
||
|
{
|
||
|
T val = (b.Y - Y) * (c.X - b.X) -
|
||
|
(b.X - X) * (c.Y - b.Y);
|
||
|
|
||
|
return val < 0;
|
||
|
}
|
||
|
|
||
|
//! Sets this vector to the linearly interpolated vector between a and b.
|
||
|
/** \param a first vector to interpolate with, maximum at 1.0f
|
||
|
\param b second vector to interpolate with, maximum at 0.0f
|
||
|
\param d Interpolation value between 0.0f (all vector b) and 1.0f (all vector a)
|
||
|
Note that this is the opposite direction of interpolation to getInterpolated_quadratic()
|
||
|
*/
|
||
|
vector2d<T> &interpolate(const vector2d<T> &a, const vector2d<T> &b, f64 d)
|
||
|
{
|
||
|
X = (T)((f64)b.X + ((a.X - b.X) * d));
|
||
|
Y = (T)((f64)b.Y + ((a.Y - b.Y) * d));
|
||
|
return *this;
|
||
|
}
|
||
|
|
||
|
//! X coordinate of vector.
|
||
|
T X;
|
||
|
|
||
|
//! Y coordinate of vector.
|
||
|
T Y;
|
||
|
};
|
||
|
|
||
|
//! Typedef for f32 2d vector.
|
||
|
typedef vector2d<f32> vector2df;
|
||
|
|
||
|
//! Typedef for integer 2d vector.
|
||
|
typedef vector2d<s32> vector2di;
|
||
|
|
||
|
template <class S, class T>
|
||
|
vector2d<T> operator*(const S scalar, const vector2d<T> &vector)
|
||
|
{
|
||
|
return vector * scalar;
|
||
|
}
|
||
|
|
||
|
// These methods are declared in dimension2d, but need definitions of vector2d
|
||
|
template <class T>
|
||
|
dimension2d<T>::dimension2d(const vector2d<T> &other) :
|
||
|
Width(other.X), Height(other.Y)
|
||
|
{
|
||
|
}
|
||
|
|
||
|
template <class T>
|
||
|
bool dimension2d<T>::operator==(const vector2d<T> &other) const
|
||
|
{
|
||
|
return Width == other.X && Height == other.Y;
|
||
|
}
|
||
|
|
||
|
} // end namespace core
|
||
|
} // end namespace irr
|
||
|
|
||
|
namespace std
|
||
|
{
|
||
|
|
||
|
template <class T>
|
||
|
struct hash<irr::core::vector2d<T>>
|
||
|
{
|
||
|
size_t operator()(const irr::core::vector2d<T> &vec) const
|
||
|
{
|
||
|
size_t h1 = hash<T>()(vec.X);
|
||
|
size_t h2 = hash<T>()(vec.Y);
|
||
|
return (h1 << (4 * sizeof(h1)) | h1 >> (4 * sizeof(h1))) ^ h2;
|
||
|
}
|
||
|
};
|
||
|
|
||
|
}
|