331 lines
10 KiB
C++
331 lines
10 KiB
C++
/* 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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#include "precompiled.h"
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#include "Geometry.h"
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#include "maths/FixedVector2D.h"
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using namespace Geometry;
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// TODO: all of these things could be optimised quite easily
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bool Geometry::PointIsInSquare(CFixedVector2D point, CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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fixed du = point.Dot(u);
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if (-halfSize.X <= du && du <= halfSize.X)
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{
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fixed dv = point.Dot(v);
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if (-halfSize.Y <= dv && dv <= halfSize.Y)
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return true;
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}
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return false;
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}
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CFixedVector2D Geometry::GetHalfBoundingBox(CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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return CFixedVector2D(
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u.X.Multiply(halfSize.X).Absolute() + v.X.Multiply(halfSize.Y).Absolute(),
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u.Y.Multiply(halfSize.X).Absolute() + v.Y.Multiply(halfSize.Y).Absolute()
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);
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}
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fixed Geometry::DistanceToSquare(CFixedVector2D point, CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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/*
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* Relative to its own coordinate system, we have a square like:
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*
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* A : B : C
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* : :
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* - - ########### - -
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* # #
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* # I #
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* D # 0 # E v
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* # # ^
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* # # |
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* - - ########### - - -->u
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* : :
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* F : G : H
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*
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* where 0 is the center, u and v are unit axes,
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* and the square is hw*2 by hh*2 units in size.
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*
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* Points in the BIG regions should check distance to horizontal edges.
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* Points in the DIE regions should check distance to vertical edges.
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* Points in the ACFH regions should check distance to the corresponding corner.
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*
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* So we just need to check all of the regions to work out which calculations to apply.
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*
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*/
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// du, dv are the location of the point in the square's coordinate system
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fixed du = point.Dot(u);
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fixed dv = point.Dot(v);
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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// TODO: I haven't actually tested this
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if (-hw < du && du < hw) // regions B, I, G
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{
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fixed closest = (dv.Absolute() - hh).Absolute(); // horizontal edges
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if (-hh < dv && dv < hh) // region I
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closest = std::min(closest, (du.Absolute() - hw).Absolute()); // vertical edges
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return closest;
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}
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else if (-hh < dv && dv < hh) // regions D, E
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{
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return (du.Absolute() - hw).Absolute(); // vertical edges
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}
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else // regions A, C, F, H
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{
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CFixedVector2D corner;
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if (du < fixed::Zero()) // A, F
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corner -= u.Multiply(hw);
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else // C, H
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corner += u.Multiply(hw);
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if (dv < fixed::Zero()) // F, H
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corner -= v.Multiply(hh);
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else // A, C
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corner += v.Multiply(hh);
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return (corner - point).Length();
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}
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}
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CFixedVector2D Geometry::NearestPointOnSquare(CFixedVector2D point, CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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/*
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* Relative to its own coordinate system, we have a square like:
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*
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* A : : C
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* : :
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* - - #### B #### - -
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* #\ /#
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* # \ / #
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* D --0-- E v
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* # / \ # ^
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* #/ \# |
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* - - #### G #### - - -->u
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* : :
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* F : : H
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*
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* where 0 is the center, u and v are unit axes,
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* and the square is hw*2 by hh*2 units in size.
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*
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* Points in the BDEG regions are nearest to the corresponding edge.
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* Points in the ACFH regions are nearest to the corresponding corner.
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*
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* So we just need to check all of the regions to work out which calculations to apply.
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*
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*/
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// du, dv are the location of the point in the square's coordinate system
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fixed du = point.Dot(u);
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fixed dv = point.Dot(v);
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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if (-hw < du && du < hw) // regions B, G; or regions D, E inside the square
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{
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if (-hh < dv && dv < hh && (du.Absolute() - hw).Absolute() < (dv.Absolute() - hh).Absolute()) // regions D, E
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{
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if (du >= fixed::Zero()) // E
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return u.Multiply(hw) + v.Multiply(dv);
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else // D
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return -u.Multiply(hw) + v.Multiply(dv);
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}
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else // B, G
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{
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if (dv >= fixed::Zero()) // B
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return v.Multiply(hh) + u.Multiply(du);
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else // G
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return -v.Multiply(hh) + u.Multiply(du);
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}
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}
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else if (-hh < dv && dv < hh) // regions D, E outside the square
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{
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if (du >= fixed::Zero()) // E
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return u.Multiply(hw) + v.Multiply(dv);
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else // D
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return -u.Multiply(hw) + v.Multiply(dv);
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}
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else // regions A, C, F, H
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{
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CFixedVector2D corner;
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if (du < fixed::Zero()) // A, F
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corner -= u.Multiply(hw);
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else // C, H
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corner += u.Multiply(hw);
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if (dv < fixed::Zero()) // F, H
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corner -= v.Multiply(hh);
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else // A, C
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corner += v.Multiply(hh);
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return corner;
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}
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}
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bool Geometry::TestRaySquare(CFixedVector2D a, CFixedVector2D b, CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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/*
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* We only consider collisions to be when the ray goes from outside to inside the shape (and possibly out again).
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* Various cases to consider:
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* 'a' inside, 'b' inside -> no collision
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* 'a' inside, 'b' outside -> no collision
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* 'a' outside, 'b' inside -> collision
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* 'a' outside, 'b' outside -> depends; use separating axis theorem:
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* if the ray's bounding box is outside the square -> no collision
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* if the whole square is on the same side of the ray -> no collision
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* otherwise -> collision
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* (Points on the edge are considered 'inside'.)
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*/
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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fixed au = a.Dot(u);
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fixed av = a.Dot(v);
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if (-hw <= au && au <= hw && -hh <= av && av <= hh)
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return false; // a is inside
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fixed bu = b.Dot(u);
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fixed bv = b.Dot(v);
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if (-hw <= bu && bu <= hw && -hh <= bv && bv <= hh) // TODO: isn't this subsumed by the next checks?
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return true; // a is outside, b is inside
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if ((au < -hw && bu < -hw) || (au > hw && bu > hw) || (av < -hh && bv < -hh) || (av > hh && bv > hh))
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return false; // ab is entirely above/below/side the square
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CFixedVector2D abp = (b - a).Perpendicular();
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fixed s0 = abp.Dot((u.Multiply(hw) + v.Multiply(hh)) - a);
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fixed s1 = abp.Dot((u.Multiply(hw) - v.Multiply(hh)) - a);
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fixed s2 = abp.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a);
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fixed s3 = abp.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a);
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if (s0.IsZero() || s1.IsZero() || s2.IsZero() || s3.IsZero())
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return true; // ray intersects the corner
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bool sign = (s0 < fixed::Zero());
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if ((s1 < fixed::Zero()) != sign || (s2 < fixed::Zero()) != sign || (s3 < fixed::Zero()) != sign)
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return true; // ray cuts through the square
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return false;
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}
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bool Geometry::TestRayAASquare(CFixedVector2D a, CFixedVector2D b, CFixedVector2D halfSize)
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{
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// Exactly like TestRaySquare with u=(1,0), v=(0,1)
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// Assume the compiler is clever enough to inline and simplify all this
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// (TODO: stop assuming that)
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CFixedVector2D u (fixed::FromInt(1), fixed::Zero());
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CFixedVector2D v (fixed::Zero(), fixed::FromInt(1));
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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fixed au = a.Dot(u);
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fixed av = a.Dot(v);
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if (-hw <= au && au <= hw && -hh <= av && av <= hh)
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return false; // a is inside
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fixed bu = b.Dot(u);
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fixed bv = b.Dot(v);
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if (-hw <= bu && bu <= hw && -hh <= bv && bv <= hh) // TODO: isn't this subsumed by the next checks?
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return true; // a is outside, b is inside
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if ((au < -hw && bu < -hw) || (au > hw && bu > hw) || (av < -hh && bv < -hh) || (av > hh && bv > hh))
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return false; // ab is entirely above/below/side the square
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CFixedVector2D abp = (b - a).Perpendicular();
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fixed s0 = abp.Dot((u.Multiply(hw) + v.Multiply(hh)) - a);
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fixed s1 = abp.Dot((u.Multiply(hw) - v.Multiply(hh)) - a);
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fixed s2 = abp.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a);
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fixed s3 = abp.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a);
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if (s0.IsZero() || s1.IsZero() || s2.IsZero() || s3.IsZero())
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return true; // ray intersects the corner
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bool sign = (s0 < fixed::Zero());
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if ((s1 < fixed::Zero()) != sign || (s2 < fixed::Zero()) != sign || (s3 < fixed::Zero()) != sign)
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return true; // ray cuts through the square
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return false;
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}
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/**
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* Separating axis test; returns true if the square defined by u/v/halfSize at the origin
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* is not entirely on the clockwise side of a line in direction 'axis' passing through 'a'
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*/
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static bool SquareSAT(CFixedVector2D a, CFixedVector2D axis, CFixedVector2D u, CFixedVector2D v, CFixedVector2D halfSize)
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{
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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CFixedVector2D p = axis.Perpendicular();
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if (p.Dot((u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
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return true;
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if (p.Dot((u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
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return true;
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if (p.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
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return true;
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if (p.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
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return true;
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return false;
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}
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bool Geometry::TestSquareSquare(
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CFixedVector2D c0, CFixedVector2D u0, CFixedVector2D v0, CFixedVector2D halfSize0,
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CFixedVector2D c1, CFixedVector2D u1, CFixedVector2D v1, CFixedVector2D halfSize1)
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{
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// TODO: need to test this carefully
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CFixedVector2D corner0a = c0 + u0.Multiply(halfSize0.X) + v0.Multiply(halfSize0.Y);
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CFixedVector2D corner0b = c0 - u0.Multiply(halfSize0.X) - v0.Multiply(halfSize0.Y);
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CFixedVector2D corner1a = c1 + u1.Multiply(halfSize1.X) + v1.Multiply(halfSize1.Y);
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CFixedVector2D corner1b = c1 - u1.Multiply(halfSize1.X) - v1.Multiply(halfSize1.Y);
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// Do a SAT test for each square vs each edge of the other square
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if (!SquareSAT(corner0a - c1, -u0, u1, v1, halfSize1))
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return false;
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if (!SquareSAT(corner0a - c1, v0, u1, v1, halfSize1))
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return false;
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if (!SquareSAT(corner0b - c1, u0, u1, v1, halfSize1))
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return false;
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if (!SquareSAT(corner0b - c1, -v0, u1, v1, halfSize1))
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return false;
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if (!SquareSAT(corner1a - c0, -u1, u0, v0, halfSize0))
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return false;
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if (!SquareSAT(corner1a - c0, v1, u0, v0, halfSize0))
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return false;
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if (!SquareSAT(corner1b - c0, u1, u0, v0, halfSize0))
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return false;
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if (!SquareSAT(corner1b - c0, -v1, u0, v0, halfSize0))
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return false;
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return true;
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}
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