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157c6af18e
Avoid cases of filenames Update years in terms and other legal(ish) documents Don't update years in license headers, since change is not meaningful Will add linter rule in seperate commit Happy recompiling everyone! Original Patch By: Nescio Comment By: Gallaecio Differential Revision: D2620 This was SVN commit r27786.
459 lines
16 KiB
C++
459 lines
16 KiB
C++
/* Copyright (C) 2020 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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namespace Geometry
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{
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// TODO: all of these things could be optimised quite easily
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CFixedVector2D GetHalfBoundingBox(const CFixedVector2D& u, const CFixedVector2D& v, const 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 DistanceToSquare(const CFixedVector2D& point, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize, bool countInsideAsZero)
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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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// By symmetry (taking absolute values), we work only in the 0-B-C-E quadrant
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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).Absolute();
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fixed dv = point.Dot(v).Absolute();
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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if (du < hw) // regions B, I, G
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{
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if (dv < hh) // region I
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return countInsideAsZero ? fixed::Zero() : std::min(hw - du, hh - dv);
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else
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return dv - hh;
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}
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else if (dv < hh) // regions D, E
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{
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return du - hw; // 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 distance(du - hw, dv - hh);
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return distance.Length();
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}
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}
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// Same as above except it does not use Length
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// For explanations refer to DistanceToSquare
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fixed DistanceToSquareSquared(const CFixedVector2D& point, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize, bool countInsideAsZero)
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{
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fixed du = point.Dot(u).Absolute();
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fixed dv = point.Dot(v).Absolute();
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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if (du < hw) // regions B, I, G
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{
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if (dv < hh) // region I
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return countInsideAsZero ? fixed::Zero() : std::min((hw - du).Square(), (hh - dv).Square());
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else
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return (dv - hh).Square(); // horizontal edges
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}
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else if (dv < hh) // regions D, E
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{
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return (du - hw).Square(); // vertical edges
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}
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else // regions A, C, F, H
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{
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return (du - hw).Square() + (dv - hh).Square();
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}
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}
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CFixedVector2D NearestPointOnSquare(const CFixedVector2D& point, const CFixedVector2D& u, const CFixedVector2D& v, const 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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fixed DistanceSquareToSquare(const CFixedVector2D& relativePos, const CFixedVector2D& u1, const CFixedVector2D& v1, const CFixedVector2D& halfSize1, const CFixedVector2D& u2, const CFixedVector2D& v2, const CFixedVector2D& halfSize2)
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{
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/*
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* The shortest distance between two non colliding squares equals the distance between a corner
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* and other square. Thus calculating all 8 those distances and taking the smallest.
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* For colliding squares we simply return 0. When one of the points is inside the other square
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* we depend on DistanceToSquare's countInsideAsZero. When no point is inside the other square,
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* it is enough to check that two adjacent edges of one square does not collide with the other square.
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*/
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fixed hw1 = halfSize1.X;
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fixed hh1 = halfSize1.Y;
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fixed hw2 = halfSize2.X;
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fixed hh2 = halfSize2.Y;
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if (TestRaySquare(relativePos + u1.Multiply(hw1) + v1.Multiply(hh1), relativePos - u1.Multiply(hw1) + v1.Multiply(hh1), u2, v2, halfSize2) ||
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TestRaySquare(relativePos + u1.Multiply(hw1) + v1.Multiply(hh1), relativePos + u1.Multiply(hw1) - v1.Multiply(hh1), u2, v2, halfSize2))
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return fixed::Zero();
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return std::min(std::min(std::min(
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DistanceToSquare(relativePos + u1.Multiply(hw1) + v1.Multiply(hh1), u2, v2, halfSize2, true),
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DistanceToSquare(relativePos + u1.Multiply(hw1) - v1.Multiply(hh1), u2, v2, halfSize2, true)),
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std::min(
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DistanceToSquare(relativePos - u1.Multiply(hw1) + v1.Multiply(hh1), u2, v2, halfSize2, true),
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DistanceToSquare(relativePos - u1.Multiply(hw1) - v1.Multiply(hh1), u2, v2, halfSize2, true))),
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std::min(std::min(
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DistanceToSquare(relativePos + u2.Multiply(hw2) + v2.Multiply(hh2), u1, v1, halfSize1, true),
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DistanceToSquare(relativePos + u2.Multiply(hw2) - v2.Multiply(hh2), u1, v1, halfSize1, true)),
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std::min(
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DistanceToSquare(relativePos - u2.Multiply(hw2) + v2.Multiply(hh2), u1, v1, halfSize1, true),
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DistanceToSquare(relativePos - u2.Multiply(hw2) - v2.Multiply(hh2), u1, v1, halfSize1, true))));
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}
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fixed MaxDistanceToSquare(const CFixedVector2D& point, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize, bool countInsideAsZero)
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{
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fixed hw = halfSize.X;
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fixed hh = halfSize.Y;
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if (point.Dot(u).Absolute() < hw && point.Dot(v).Absolute() < hh && countInsideAsZero)
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return fixed::Zero();
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/*
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* The maximum distance from a point to an edge of a square equals the greatest distance
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* from the point to the a corner. Thus calculating all and taking the greatest.
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*/
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return std::max(std::max(
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(point + u.Multiply(hw) + v.Multiply(hh)).Length(),
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(point + u.Multiply(hw) - v.Multiply(hh)).Length()),
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std::max(
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(point - u.Multiply(hw) + v.Multiply(hh)).Length(),
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(point - u.Multiply(hw) - v.Multiply(hh)).Length()));
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}
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fixed MaxDistanceSquareToSquare(const CFixedVector2D& relativePos, const CFixedVector2D& u1, const CFixedVector2D& v1, const CFixedVector2D& halfSize1, const CFixedVector2D& u2, const CFixedVector2D& v2, const CFixedVector2D& halfSize2)
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{
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/*
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* The maximum distance from an edge of a square to the edge of another square
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* equals the greatest distance from the any of the 16 corner corner distances.
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*/
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fixed hw1 = halfSize1.X;
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fixed hh1 = halfSize1.Y;
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return std::max(std::max(
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MaxDistanceToSquare(relativePos + u1.Multiply(hw1) + v1.Multiply(hh1), u2, v2, halfSize2, true),
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MaxDistanceToSquare(relativePos + u1.Multiply(hw1) - v1.Multiply(hh1), u2, v2, halfSize2, true)),
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std::max(MaxDistanceToSquare(relativePos - u1.Multiply(hw1) + v1.Multiply(hh1), u2, v2, halfSize2, true),
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MaxDistanceToSquare(relativePos - u1.Multiply(hw1) - v1.Multiply(hh1), u2, v2, halfSize2, true)));
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}
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bool TestRaySquare(const CFixedVector2D& a, const CFixedVector2D& b, const CFixedVector2D& u, const CFixedVector2D& v, const 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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// Exactly like TestRaySquare with u=(1,0), v=(0,1)
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bool TestRayAASquare(const CFixedVector2D& a, const CFixedVector2D& b, const 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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if (-hw <= a.X && a.X <= hw && -hh <= a.Y && a.Y <= hh)
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return false; // a is inside
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if (-hw <= b.X && b.X <= hw && -hh <= b.Y && b.Y <= 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 ((a.X < -hw && b.X < -hw) || (a.X > hw && b.X > hw) || (a.Y < -hh && b.Y < -hh) || (a.Y > hh && b.Y > 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(CFixedVector2D(hw, hh) - a);
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fixed s1 = abp.Dot(CFixedVector2D(hw, -hh) - a);
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fixed s2 = abp.Dot(CFixedVector2D(-hw, -hh) - a);
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fixed s3 = abp.Dot(CFixedVector2D(-hw, 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(const CFixedVector2D& a, const CFixedVector2D& axis, const CFixedVector2D& u, const CFixedVector2D& v, const 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.RelativeOrientation(u.Multiply(hw) + v.Multiply(hh) - a) <= 0)
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return true;
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if (p.RelativeOrientation(u.Multiply(hw) - v.Multiply(hh) - a) <= 0)
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return true;
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if (p.RelativeOrientation(-u.Multiply(hw) - v.Multiply(hh) - a) <= 0)
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return true;
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if (p.RelativeOrientation(-u.Multiply(hw) + v.Multiply(hh) - a) <= 0)
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return true;
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return false;
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}
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bool TestSquareSquare(
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const CFixedVector2D& c0, const CFixedVector2D& u0, const CFixedVector2D& v0, const CFixedVector2D& halfSize0,
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const CFixedVector2D& c1, const CFixedVector2D& u1, const CFixedVector2D& v1, const 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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int GetPerimeterDistance(int x_max, int y_max, int x, int y)
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{
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if (x_max <= 0 || y_max <= 0)
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return 0;
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int quarter = x_max + y_max;
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if (x == x_max && y >= 0)
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return y;
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if (y == y_max)
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return quarter - x;
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if (x == -x_max)
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return 2 * quarter - y;
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if (y == -y_max)
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return 3 * quarter + x;
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if (x == x_max)
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return 4 * quarter + y;
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return 0;
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}
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std::pair<int, int> GetPerimeterCoordinates(int x_max, int y_max, int k)
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{
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if (x_max <= 0 || y_max <= 0)
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return std::pair<int, int>(0, 0);
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int quarter = x_max + y_max;
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k %= 4 * quarter;
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if (k < 0)
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k += 4 * quarter;
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if (k < y_max)
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return std::pair<int, int>(x_max, k);
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if (k < quarter + x_max)
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return std::pair<int, int>(quarter - k, y_max);
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if (k < 2 * quarter + y_max)
|
||
return std::pair<int, int>(-x_max, 2 * quarter - k);
|
||
if (k < 3 * quarter + x_max)
|
||
return std::pair<int, int>(k - 3 * quarter, -y_max);
|
||
return std::pair<int, int>(x_max, k - 4 * quarter);
|
||
}
|
||
|
||
fixed DistanceToSegment(
|
||
const CFixedVector2D& point, const CFixedVector2D& a, const CFixedVector2D& b)
|
||
{
|
||
// First we need to figure out from which part of the segment we should
|
||
// calculate distance.
|
||
// We split 2D space in three spaces:
|
||
// | |
|
||
// 1 | 2 | 3
|
||
// A--------------------------------B
|
||
// Here we need | Between A and B we need to | Here we need
|
||
// distance to A | calculate distance to the line | distance to B
|
||
//
|
||
const CFixedVector2D dir = b - a;
|
||
// We project the point, point A, and point B upon the direction of the
|
||
// segment to figure out in which space the point is.
|
||
const fixed pointDot = dir.Dot(point);
|
||
const fixed aDot = dir.Dot(a);
|
||
// The point is lying in space #1.
|
||
if (pointDot <= aDot)
|
||
return (point - a).Length();
|
||
const fixed bDot = dir.Dot(b);
|
||
// The point is lying in space #3.
|
||
if (pointDot >= bDot)
|
||
return (point - b).Length();
|
||
// The point is lying in space #2.
|
||
CFixedVector2D normal = dir.Perpendicular();
|
||
normal.Normalize();
|
||
return (normal.Dot(a) - normal.Dot(point)).Absolute();
|
||
}
|
||
|
||
} // namespace Geometry
|