2024-03-21 20:13:15 +01:00
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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 <functional>
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2024-05-09 18:19:28 +02:00
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#include <array>
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2024-03-21 20:13:15 +01:00
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namespace irr
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{
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namespace core
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{
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//! 3d vector template class with lots of operators and methods.
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/** The vector3d class is used in Irrlicht for three main purposes:
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1) As a direction vector (most of the methods assume this).
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2) As a position in 3d space (which is synonymous with a direction vector from the origin to this position).
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3) To hold three Euler rotations, where X is pitch, Y is yaw and Z is roll.
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*/
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template <class T>
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class vector3d
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{
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public:
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//! Default constructor (null vector).
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constexpr vector3d() :
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X(0), Y(0), Z(0) {}
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//! Constructor with three different values
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constexpr vector3d(T nx, T ny, T nz) :
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X(nx), Y(ny), Z(nz) {}
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//! Constructor with the same value for all elements
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explicit constexpr vector3d(T n) :
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X(n), Y(n), Z(n) {}
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//! Array - vector conversion
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constexpr vector3d(const std::array<T, 3> &arr) :
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X(arr[0]), Y(arr[1]), Z(arr[2]) {}
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2024-03-21 20:13:15 +01:00
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// operators
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vector3d<T> operator-() const { return vector3d<T>(-X, -Y, -Z); }
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vector3d<T> operator+(const vector3d<T> &other) const { return vector3d<T>(X + other.X, Y + other.Y, Z + other.Z); }
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vector3d<T> &operator+=(const vector3d<T> &other)
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{
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X += other.X;
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Y += other.Y;
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Z += other.Z;
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return *this;
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}
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vector3d<T> operator+(const T val) const { return vector3d<T>(X + val, Y + val, Z + val); }
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vector3d<T> &operator+=(const T val)
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{
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X += val;
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Y += val;
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Z += val;
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return *this;
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}
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vector3d<T> operator-(const vector3d<T> &other) const { return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z); }
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vector3d<T> &operator-=(const vector3d<T> &other)
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{
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X -= other.X;
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Y -= other.Y;
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Z -= other.Z;
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return *this;
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}
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vector3d<T> operator-(const T val) const { return vector3d<T>(X - val, Y - val, Z - val); }
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vector3d<T> &operator-=(const T val)
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{
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X -= val;
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Y -= val;
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Z -= val;
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return *this;
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}
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vector3d<T> operator*(const vector3d<T> &other) const { return vector3d<T>(X * other.X, Y * other.Y, Z * other.Z); }
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vector3d<T> &operator*=(const vector3d<T> &other)
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{
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X *= other.X;
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Y *= other.Y;
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Z *= other.Z;
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return *this;
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}
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vector3d<T> operator*(const T v) const { return vector3d<T>(X * v, Y * v, Z * v); }
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vector3d<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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Z *= v;
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return *this;
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}
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vector3d<T> operator/(const vector3d<T> &other) const { return vector3d<T>(X / other.X, Y / other.Y, Z / other.Z); }
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vector3d<T> &operator/=(const vector3d<T> &other)
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{
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X /= other.X;
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Y /= other.Y;
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Z /= other.Z;
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return *this;
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}
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vector3d<T> operator/(const T v) const { return vector3d<T>(X / v, Y / v, Z / v); }
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vector3d<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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Z /= 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 > 2) // 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 > 2) // access violation
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return *(&X + index);
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}
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//! sort in order X, Y, Z.
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constexpr bool operator<=(const vector3d<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, Z.
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constexpr bool operator>=(const vector3d<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, Z.
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constexpr bool operator<(const vector3d<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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(X == other.X && Y == other.Y && Z < other.Z);
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}
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//! sort in order X, Y, Z.
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constexpr bool operator>(const vector3d<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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(X == other.X && Y == other.Y && Z > other.Z);
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}
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constexpr bool operator==(const vector3d<T> &other) const
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{
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return X == other.X && Y == other.Y && Z == other.Z;
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}
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constexpr bool operator!=(const vector3d<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 vector3d<T> &other) const
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{
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return core::equals(X, other.X) && core::equals(Y, other.Y) && core::equals(Z, other.Z);
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}
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vector3d<T> &set(const T nx, const T ny, const T nz)
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{
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X = nx;
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Y = ny;
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Z = nz;
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return *this;
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}
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vector3d<T> &set(const vector3d<T> &p)
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{
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X = p.X;
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Y = p.Y;
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Z = p.Z;
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return *this;
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}
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2024-05-09 18:19:28 +02:00
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std::array<T, 3> toArray() const {
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return {X, Y, Z};
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}
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2024-03-21 20:13:15 +01:00
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//! Get length of the vector.
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T getLength() const { return core::squareroot(X * X + Y * Y + Z * Z); }
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//! Get squared length of the vector.
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/** This is useful because it is much faster than getLength().
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\return Squared length of the vector. */
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T getLengthSQ() const { return X * X + Y * Y + Z * Z; }
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//! Get the dot product with another vector.
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T dotProduct(const vector3d<T> &other) const
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{
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return X * other.X + Y * other.Y + Z * other.Z;
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}
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//! Get distance from another point.
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/** Here, the vector is interpreted as point in 3 dimensional space. */
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T getDistanceFrom(const vector3d<T> &other) const
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{
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return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).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 point in 3 dimensional space. */
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T getDistanceFromSQ(const vector3d<T> &other) const
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{
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return vector3d<T>(X - other.X, Y - other.Y, Z - other.Z).getLengthSQ();
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}
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//! Calculates the cross product with another vector.
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/** \param p Vector to multiply with.
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\return Cross product of this vector with p. */
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vector3d<T> crossProduct(const vector3d<T> &p) const
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{
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return vector3d<T>(Y * p.Z - Z * p.Y, Z * p.X - X * p.Z, X * p.Y - Y * p.X);
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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 vector3d<T> &begin, const vector3d<T> &end) const
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{
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const T f = (end - begin).getLengthSQ();
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return getDistanceFromSQ(begin) <= f &&
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getDistanceFromSQ(end) <= f;
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}
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//! Normalizes the vector.
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/** In case of the 0 vector the result is still 0, otherwise
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the length of the vector will be 1.
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\return Reference to this vector after normalization. */
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vector3d<T> &normalize()
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{
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f64 length = X * X + Y * Y + Z * Z;
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if (length == 0) // this check isn't an optimization but prevents getting NAN in the sqrt.
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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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Z = (T)(Z * length);
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return *this;
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}
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//! Sets the length of the vector to a new value
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vector3d<T> &setLength(T newlength)
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{
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normalize();
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return (*this *= newlength);
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}
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//! Inverts the vector.
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vector3d<T> &invert()
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{
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X *= -1;
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Y *= -1;
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Z *= -1;
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return *this;
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}
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//! Rotates the vector by a specified number of degrees around the Y axis and the specified center.
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/** CAREFUL: For historical reasons rotateXZBy uses a right-handed rotation
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(maybe to make it more similar to the 2D vector rotations which are counterclockwise).
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To have this work the same way as rest of Irrlicht (nodes, matrices, other rotateBy functions) pass -1*degrees in here.
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\param degrees Number of degrees to rotate around the Y axis.
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\param center The center of the rotation. */
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void rotateXZBy(f64 degrees, const vector3d<T> ¢er = vector3d<T>())
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{
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degrees *= DEGTORAD64;
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f64 cs = cos(degrees);
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f64 sn = sin(degrees);
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X -= center.X;
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Z -= center.Z;
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set((T)(X * cs - Z * sn), Y, (T)(X * sn + Z * cs));
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X += center.X;
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Z += center.Z;
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}
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//! Rotates the vector by a specified number of degrees around the Z axis and the specified center.
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/** \param degrees: Number of degrees to rotate around the Z axis.
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\param center: The center of the rotation. */
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void rotateXYBy(f64 degrees, const vector3d<T> ¢er = vector3d<T>())
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{
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degrees *= DEGTORAD64;
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f64 cs = cos(degrees);
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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), Z);
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X += center.X;
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Y += center.Y;
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}
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//! Rotates the vector by a specified number of degrees around the X axis and the specified center.
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/** \param degrees: Number of degrees to rotate around the X axis.
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\param center: The center of the rotation. */
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void rotateYZBy(f64 degrees, const vector3d<T> ¢er = vector3d<T>())
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{
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degrees *= DEGTORAD64;
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f64 cs = cos(degrees);
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f64 sn = sin(degrees);
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Z -= center.Z;
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Y -= center.Y;
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set(X, (T)(Y * cs - Z * sn), (T)(Y * sn + Z * cs));
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Z += center.Z;
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Y += center.Y;
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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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vector3d<T> getInterpolated(const vector3d<T> &other, f64 d) const
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{
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const f64 inv = 1.0 - d;
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return vector3d<T>((T)(other.X * inv + X * d), (T)(other.Y * inv + Y * d), (T)(other.Z * inv + Z * 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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vector3d<T> getInterpolated_quadratic(const vector3d<T> &v2, const vector3d<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 = (T)1.0 - d;
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const f64 mul0 = inv * inv;
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const f64 mul1 = (T)2.0 * d * inv;
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const f64 mul2 = d * d;
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return vector3d<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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(T)(Z * mul0 + v2.Z * mul1 + v3.Z * 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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vector3d<T> &interpolate(const vector3d<T> &a, const vector3d<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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Z = (T)((f64)b.Z + ((a.Z - b.Z) * d));
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return *this;
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}
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//! Get the rotations that would make a (0,0,1) direction vector point in the same direction as this direction vector.
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/** Thanks to Arras on the Irrlicht forums for this method. This utility method is very useful for
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orienting scene nodes towards specific targets. For example, if this vector represents the difference
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between two scene nodes, then applying the result of getHorizontalAngle() to one scene node will point
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it at the other one.
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Example code:
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// Where target and seeker are of type ISceneNode*
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const vector3df toTarget(target->getAbsolutePosition() - seeker->getAbsolutePosition());
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const vector3df requiredRotation = toTarget.getHorizontalAngle();
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seeker->setRotation(requiredRotation);
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\return A rotation vector containing the X (pitch) and Y (raw) rotations (in degrees) that when applied to a
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+Z (e.g. 0, 0, 1) direction vector would make it point in the same direction as this vector. The Z (roll) rotation
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is always 0, since two Euler rotations are sufficient to point in any given direction. */
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vector3d<T> getHorizontalAngle() const
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{
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vector3d<T> angle;
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// tmp avoids some precision troubles on some compilers when working with T=s32
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f64 tmp = (atan2((f64)X, (f64)Z) * RADTODEG64);
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angle.Y = (T)tmp;
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if (angle.Y < 0)
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angle.Y += 360;
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if (angle.Y >= 360)
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angle.Y -= 360;
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const f64 z1 = core::squareroot(X * X + Z * Z);
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tmp = (atan2((f64)z1, (f64)Y) * RADTODEG64 - 90.0);
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angle.X = (T)tmp;
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if (angle.X < 0)
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angle.X += 360;
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if (angle.X >= 360)
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angle.X -= 360;
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return angle;
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}
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//! Get the spherical coordinate angles
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/** This returns Euler degrees for the point represented by
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this vector. The calculation assumes the pole at (0,1,0) and
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returns the angles in X and Y.
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*/
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vector3d<T> getSphericalCoordinateAngles() const
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{
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vector3d<T> angle;
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const f64 length = X * X + Y * Y + Z * Z;
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if (length) {
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if (X != 0) {
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angle.Y = (T)(atan2((f64)Z, (f64)X) * RADTODEG64);
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} else if (Z < 0)
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angle.Y = 180;
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angle.X = (T)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64);
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}
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return angle;
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}
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//! Builds a direction vector from (this) rotation vector.
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/** This vector is assumed to be a rotation vector composed of 3 Euler angle rotations, in degrees.
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The implementation performs the same calculations as using a matrix to do the rotation.
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\param[in] forwards The direction representing "forwards" which will be rotated by this vector.
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If you do not provide a direction, then the +Z axis (0, 0, 1) will be assumed to be forwards.
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\return A direction vector calculated by rotating the forwards direction by the 3 Euler angles
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(in degrees) represented by this vector. */
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vector3d<T> rotationToDirection(const vector3d<T> &forwards = vector3d<T>(0, 0, 1)) const
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|
{
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|
const f64 cr = cos(core::DEGTORAD64 * X);
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|
const f64 sr = sin(core::DEGTORAD64 * X);
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|
const f64 cp = cos(core::DEGTORAD64 * Y);
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const f64 sp = sin(core::DEGTORAD64 * Y);
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|
const f64 cy = cos(core::DEGTORAD64 * Z);
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|
const f64 sy = sin(core::DEGTORAD64 * Z);
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const f64 srsp = sr * sp;
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|
const f64 crsp = cr * sp;
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|
const f64 pseudoMatrix[] = {
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|
(cp * cy), (cp * sy), (-sp),
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(srsp * cy - cr * sy), (srsp * sy + cr * cy), (sr * cp),
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(crsp * cy + sr * sy), (crsp * sy - sr * cy), (cr * cp)};
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|
|
|
return vector3d<T>(
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|
(T)(forwards.X * pseudoMatrix[0] +
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|
|
forwards.Y * pseudoMatrix[3] +
|
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|
|
forwards.Z * pseudoMatrix[6]),
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|
(T)(forwards.X * pseudoMatrix[1] +
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|
forwards.Y * pseudoMatrix[4] +
|
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|
|
forwards.Z * pseudoMatrix[7]),
|
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|
|
(T)(forwards.X * pseudoMatrix[2] +
|
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|
|
forwards.Y * pseudoMatrix[5] +
|
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|
|
forwards.Z * pseudoMatrix[8]));
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|
|
}
|
|
|
|
|
|
|
|
//! Fills an array of 4 values with the vector data (usually floats).
|
|
|
|
/** Useful for setting in shader constants for example. The fourth value
|
|
|
|
will always be 0. */
|
|
|
|
void getAs4Values(T *array) const
|
|
|
|
{
|
|
|
|
array[0] = X;
|
|
|
|
array[1] = Y;
|
|
|
|
array[2] = Z;
|
|
|
|
array[3] = 0;
|
|
|
|
}
|
|
|
|
|
|
|
|
//! Fills an array of 3 values with the vector data (usually floats).
|
|
|
|
/** Useful for setting in shader constants for example.*/
|
|
|
|
void getAs3Values(T *array) const
|
|
|
|
{
|
|
|
|
array[0] = X;
|
|
|
|
array[1] = Y;
|
|
|
|
array[2] = Z;
|
|
|
|
}
|
|
|
|
|
|
|
|
//! X coordinate of the vector
|
|
|
|
T X;
|
|
|
|
|
|
|
|
//! Y coordinate of the vector
|
|
|
|
T Y;
|
|
|
|
|
|
|
|
//! Z coordinate of the vector
|
|
|
|
T Z;
|
|
|
|
};
|
|
|
|
|
|
|
|
//! partial specialization for integer vectors
|
|
|
|
// Implementer note: inline keyword needed due to template specialization for s32. Otherwise put specialization into a .cpp
|
|
|
|
template <>
|
|
|
|
inline vector3d<s32> vector3d<s32>::operator/(s32 val) const
|
|
|
|
{
|
|
|
|
return core::vector3d<s32>(X / val, Y / val, Z / val);
|
|
|
|
}
|
|
|
|
template <>
|
|
|
|
inline vector3d<s32> &vector3d<s32>::operator/=(s32 val)
|
|
|
|
{
|
|
|
|
X /= val;
|
|
|
|
Y /= val;
|
|
|
|
Z /= val;
|
|
|
|
return *this;
|
|
|
|
}
|
|
|
|
|
|
|
|
template <>
|
|
|
|
inline vector3d<s32> vector3d<s32>::getSphericalCoordinateAngles() const
|
|
|
|
{
|
|
|
|
vector3d<s32> angle;
|
|
|
|
const f64 length = X * X + Y * Y + Z * Z;
|
|
|
|
|
|
|
|
if (length) {
|
|
|
|
if (X != 0) {
|
|
|
|
angle.Y = round32((f32)(atan2((f64)Z, (f64)X) * RADTODEG64));
|
|
|
|
} else if (Z < 0)
|
|
|
|
angle.Y = 180;
|
|
|
|
|
|
|
|
angle.X = round32((f32)(acos(Y * core::reciprocal_squareroot(length)) * RADTODEG64));
|
|
|
|
}
|
|
|
|
return angle;
|
|
|
|
}
|
|
|
|
|
|
|
|
//! Typedef for a f32 3d vector.
|
|
|
|
typedef vector3d<f32> vector3df;
|
|
|
|
|
|
|
|
//! Typedef for an integer 3d vector.
|
|
|
|
typedef vector3d<s32> vector3di;
|
|
|
|
|
|
|
|
//! Function multiplying a scalar and a vector component-wise.
|
|
|
|
template <class S, class T>
|
|
|
|
vector3d<T> operator*(const S scalar, const vector3d<T> &vector)
|
|
|
|
{
|
|
|
|
return vector * scalar;
|
|
|
|
}
|
|
|
|
|
|
|
|
} // end namespace core
|
|
|
|
} // end namespace irr
|
|
|
|
|
|
|
|
namespace std
|
|
|
|
{
|
|
|
|
|
|
|
|
template <class T>
|
|
|
|
struct hash<irr::core::vector3d<T>>
|
|
|
|
{
|
|
|
|
size_t operator()(const irr::core::vector3d<T> &vec) const
|
|
|
|
{
|
|
|
|
size_t h1 = hash<T>()(vec.X);
|
|
|
|
size_t h2 = hash<T>()(vec.Y);
|
|
|
|
size_t h3 = hash<T>()(vec.Z);
|
|
|
|
return (h1 << (5 * sizeof(h1)) | h1 >> (3 * sizeof(h1))) ^ (h2 << (2 * sizeof(h2)) | h2 >> (6 * sizeof(h2))) ^ h3;
|
|
|
|
}
|
|
|
|
};
|
|
|
|
|
|
|
|
}
|