2010-01-30 14:11:58 +01:00
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/* Copyright (C) 2010 Wildfire Games.
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* This file is part of 0 A.D.
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*
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* 0 A.D. is free software: you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation, either version 2 of the License, or
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* (at your option) any later version.
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*
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* 0 A.D. is distributed in the hope that it will be useful,
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* but WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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* GNU General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with 0 A.D. If not, see <http://www.gnu.org/licenses/>.
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*/
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#ifndef INCLUDED_FIXED_VECTOR2D
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#define INCLUDED_FIXED_VECTOR2D
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#include "maths/Fixed.h"
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#include "maths/Sqrt.h"
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class CFixedVector2D
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{
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public:
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fixed X, Y;
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CFixedVector2D() { }
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CFixedVector2D(fixed X, fixed Y) : X(X), Y(Y) { }
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/// Vector equality
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bool operator==(const CFixedVector2D& v) const
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{
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return (X == v.X && Y == v.Y);
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}
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2010-04-30 01:36:05 +02:00
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/// Vector inequality
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bool operator!=(const CFixedVector2D& v) const
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{
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return (X != v.X || Y != v.Y);
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}
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2010-01-30 14:11:58 +01:00
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/// Vector addition
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CFixedVector2D operator+(const CFixedVector2D& v) const
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{
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return CFixedVector2D(X + v.X, Y + v.Y);
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}
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/// Vector subtraction
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CFixedVector2D operator-(const CFixedVector2D& v) const
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{
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return CFixedVector2D(X - v.X, Y - v.Y);
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}
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/// Negation
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CFixedVector2D operator-() const
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{
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return CFixedVector2D(-X, -Y);
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}
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/// Vector addition
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CFixedVector2D& operator+=(const CFixedVector2D& v)
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{
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*this = *this + v;
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return *this;
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}
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/// Vector subtraction
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CFixedVector2D& operator-=(const CFixedVector2D& v)
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{
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*this = *this - v;
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return *this;
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}
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2010-04-19 21:47:23 +02:00
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/// Scalar multiplication by an integer
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CFixedVector2D operator*(int n) const
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{
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return CFixedVector2D(X*n, Y*n);
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}
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/**
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* Multiply by a CFixed. Likely to overflow if both numbers are large,
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* so we use an ugly name instead of operator* to make it obvious.
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*/
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CFixedVector2D Multiply(fixed n) const
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{
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return CFixedVector2D(X.Multiply(n), Y.Multiply(n));
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}
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2010-01-30 14:11:58 +01:00
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/**
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* Returns the length of the vector.
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* Will not overflow if the result can be represented as type 'fixed'.
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*/
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fixed Length() const
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{
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// Do intermediate calculations with 64-bit ints to avoid overflows
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i64 x = (i64)X.GetInternalValue();
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i64 y = (i64)Y.GetInternalValue();
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2010-05-02 22:16:53 +02:00
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u64 xx = (u64)(x * x);
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u64 yy = (u64)(y * y);
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u64 d2 = xx + yy;
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CheckUnsignedAdditionOverflow(d2, xx, L"Overflow in CFixedVector2D::Length() part 1")
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2010-01-30 14:11:58 +01:00
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u32 d = isqrt64(d2);
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2010-05-02 22:16:53 +02:00
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CheckU32CastOverflow(d, i32, L"Overflow in CFixedVector2D::Length() part 2")
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2010-01-30 14:11:58 +01:00
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fixed r;
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r.SetInternalValue((i32)d);
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return r;
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}
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2010-07-29 22:39:23 +02:00
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/**
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* Returns -1, 0, +1 depending on whether length is less/equal/greater
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* than the argument.
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* Avoids sqrting and overflowing.
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*/
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int CompareLength(fixed cmp) const
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{
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i64 x = (i64)X.GetInternalValue(); // abs(x) <= 2^31
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i64 y = (i64)Y.GetInternalValue();
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u64 xx = (u64)(x * x); // xx <= 2^62
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u64 yy = (u64)(y * y);
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u64 d2 = xx + yy; // d2 <= 2^63 (no overflow)
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i64 c = (i64)cmp.GetInternalValue();
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u64 c2 = (u64)(c * c);
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if (d2 < c2)
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return -1;
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else if (d2 > c2)
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return +1;
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else
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return 0;
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}
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/**
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* Returns -1, 0, +1 depending on whether length is less/equal/greater
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* than the argument's length.
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* Avoids sqrting and overflowing.
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*/
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int CompareLength(const CFixedVector2D& other) const
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{
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i64 x = (i64)X.GetInternalValue();
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i64 y = (i64)Y.GetInternalValue();
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u64 d2 = (u64)(x * x) + (u64)(y * y);
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i64 ox = (i64)other.X.GetInternalValue();
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i64 oy = (i64)other.Y.GetInternalValue();
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u64 od2 = (u64)(ox * ox) + (u64)(oy * oy);
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if (d2 < od2)
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return -1;
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else if (d2 > od2)
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return +1;
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else
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return 0;
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}
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2010-04-30 01:36:05 +02:00
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bool IsZero() const
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{
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return (X.IsZero() && Y.IsZero());
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}
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2010-01-30 14:11:58 +01:00
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/**
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* Normalize the vector so that length is close to 1.
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* If length is 0, does nothing.
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*/
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void Normalize()
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{
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2010-04-30 01:36:05 +02:00
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if (!IsZero())
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2010-01-30 14:11:58 +01:00
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{
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2010-04-30 01:36:05 +02:00
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fixed l = Length();
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2010-01-30 14:11:58 +01:00
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X = X / l;
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Y = Y / l;
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}
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}
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2010-04-30 01:36:05 +02:00
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/**
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* Normalize the vector so that length is close to n.
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* If length is 0, does nothing.
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*/
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void Normalize(fixed n)
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{
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fixed l = Length();
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2010-05-02 22:32:37 +02:00
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if (!l.IsZero())
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2010-04-30 01:36:05 +02:00
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{
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2010-05-02 22:32:37 +02:00
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X = X.MulDiv(n, l);
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Y = Y.MulDiv(n, l);
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2010-04-30 01:36:05 +02:00
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}
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}
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2010-01-30 14:11:58 +01:00
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/**
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* Compute the dot product of this vector with another.
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*/
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fixed Dot(const CFixedVector2D& v)
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{
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i64 x = (i64)X.GetInternalValue() * (i64)v.X.GetInternalValue();
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i64 y = (i64)Y.GetInternalValue() * (i64)v.Y.GetInternalValue();
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2010-05-02 22:16:53 +02:00
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CheckSignedAdditionOverflow(i64, x, y, L"Overflow in CFixedVector2D::Dot() part 1", L"Underflow in CFixedVector2D::Dot() part 1")
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2010-01-30 14:11:58 +01:00
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i64 sum = x + y;
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2010-05-02 22:16:53 +02:00
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sum >>= fixed::fract_bits;
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CheckCastOverflow(sum, i32, L"Overflow in CFixedVector2D::Dot() part 2", L"Underflow in CFixedVector2D::Dot() part 2")
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2010-01-30 14:11:58 +01:00
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fixed ret;
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2010-05-02 22:16:53 +02:00
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ret.SetInternalValue((i32)sum);
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2010-01-30 14:11:58 +01:00
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return ret;
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}
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2010-04-30 01:36:05 +02:00
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CFixedVector2D Perpendicular()
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{
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return CFixedVector2D(Y, -X);
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}
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2010-09-03 11:55:14 +02:00
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/**
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* Rotate the vector by the given angle (anticlockwise).
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*/
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CFixedVector2D Rotate(fixed angle)
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{
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fixed s, c;
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sincos_approx(angle, s, c);
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return CFixedVector2D(X.Multiply(c) + Y.Multiply(s), Y.Multiply(c) - X.Multiply(s));
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}
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2010-01-30 14:11:58 +01:00
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};
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#endif // INCLUDED_FIXED_VECTOR2D
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