bool Geometry::TestSquareSquare(
const CFixedVector2D& c0, const CFixedVector2D& u0, const CFixedVector2D& v0, const CFixedVector2D& halfSize0,
const CFixedVector2D& c1, const CFixedVector2D& u1, const CFixedVector2D& v1, const CFixedVector2D& halfSize1)
{
// TODO: need to test this carefully
CFixedVector2D corner0a = c0 + u0.Multiply(halfSize0.X) + v0.Multiply(halfSize0.Y);
CFixedVector2D corner0b = c0 - u0.Multiply(halfSize0.X) - v0.Multiply(halfSize0.Y);
CFixedVector2D corner1a = c1 + u1.Multiply(halfSize1.X) + v1.Multiply(halfSize1.Y);
CFixedVector2D corner1b = c1 - u1.Multiply(halfSize1.X) - v1.Multiply(halfSize1.Y);
// Do a SAT test for each square vs each edge of the other square
if (!SquareSAT(corner0a - c1, -u0, u1, v1, halfSize1))
return false;
if (!SquareSAT(corner0a - c1, v0, u1, v1, halfSize1))
return false;
if (!SquareSAT(corner0b - c1, u0, u1, v1, halfSize1))
return false;
if (!SquareSAT(corner0b - c1, -v0, u1, v1, halfSize1))
return false;
if (!SquareSAT(corner1a - c0, -u1, u0, v0, halfSize0))
return false;
if (!SquareSAT(corner1a - c0, v1, u0, v0, halfSize0))
return false;
if (!SquareSAT(corner1b - c0, u1, u0, v0, halfSize0))
return false;
if (!SquareSAT(corner1b - c0, -v1, u0, v0, halfSize0))
return false;
return true;
}
bool Geometry::TestRaySquare(const CFixedVector2D& a, const CFixedVector2D& b, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize)
{
/*
* We only consider collisions to be when the ray goes from outside to inside the shape (and possibly out again).
* Various cases to consider:
* 'a' inside, 'b' inside -> no collision
* 'a' inside, 'b' outside -> no collision
* 'a' outside, 'b' inside -> collision
* 'a' outside, 'b' outside -> depends; use separating axis theorem:
* if the ray's bounding box is outside the square -> no collision
* if the whole square is on the same side of the ray -> no collision
* otherwise -> collision
* (Points on the edge are considered 'inside'.)
*/
fixed hw = halfSize.X;
fixed hh = halfSize.Y;
fixed au = a.Dot(u);
fixed av = a.Dot(v);
if (-hw <= au && au <= hw && -hh <= av && av <= hh)
return false; // a is inside
fixed bu = b.Dot(u);
fixed bv = b.Dot(v);
if (-hw <= bu && bu <= hw && -hh <= bv && bv <= hh) // TODO: isn't this subsumed by the next checks?
return true; // a is outside, b is inside
if ((au < -hw && bu < -hw) || (au > hw && bu > hw) || (av < -hh && bv < -hh) || (av > hh && bv > hh))
return false; // ab is entirely above/below/side the square
CFixedVector2D abp = (b - a).Perpendicular();
fixed s0 = abp.Dot((u.Multiply(hw) + v.Multiply(hh)) - a);
fixed s1 = abp.Dot((u.Multiply(hw) - v.Multiply(hh)) - a);
fixed s2 = abp.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a);
fixed s3 = abp.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a);
if (s0.IsZero() || s1.IsZero() || s2.IsZero() || s3.IsZero())
return true; // ray intersects the corner
bool sign = (s0 < fixed::Zero());
if ((s1 < fixed::Zero()) != sign || (s2 < fixed::Zero()) != sign || (s3 < fixed::Zero()) != sign)
return true; // ray cuts through the square
return false;
}
/**
* Separating axis test; returns true if the square defined by u/v/halfSize at the origin
* is not entirely on the clockwise side of a line in direction 'axis' passing through 'a'
*/
static bool SquareSAT(const CFixedVector2D& a, const CFixedVector2D& axis, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize)
{
fixed hw = halfSize.X;
fixed hh = halfSize.Y;
CFixedVector2D p = axis.Perpendicular();
if (p.Dot((u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
return true;
if (p.Dot((u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
return true;
if (p.Dot((-u.Multiply(hw) - v.Multiply(hh)) - a) <= fixed::Zero())
return true;
if (p.Dot((-u.Multiply(hw) + v.Multiply(hh)) - a) <= fixed::Zero())
return true;
return false;
}
virtual CFixedVector3D PickSpawnPoint(entity_id_t spawned)
{
// Try to find a free space around the building's footprint.
// (Note that we use the footprint, not the obstruction shape - this might be a bit dodgy
// because the footprint might be inside the obstruction, but it hopefully gives us a nicer
// shape.)
const CFixedVector3D error(fixed::FromInt(-1), fixed::FromInt(-1), fixed::FromInt(-1));
CmpPtr<ICmpPosition> cmpPosition(GetSimContext(), GetEntityId());
if (!cmpPosition || !cmpPosition->IsInWorld())
return error;
CmpPtr<ICmpObstructionManager> cmpObstructionManager(GetSimContext(), SYSTEM_ENTITY);
if (!cmpObstructionManager)
return error;
entity_pos_t spawnedRadius;
ICmpObstructionManager::tag_t spawnedTag;
CmpPtr<ICmpObstruction> cmpSpawnedObstruction(GetSimContext(), spawned);
if (cmpSpawnedObstruction)
{
spawnedRadius = cmpSpawnedObstruction->GetUnitRadius();
spawnedTag = cmpSpawnedObstruction->GetObstruction();
}
// else use zero radius
// Get passability class from UnitMotion
CmpPtr<ICmpUnitMotion> cmpUnitMotion(GetSimContext(), spawned);
if (!cmpUnitMotion)
return error;
ICmpPathfinder::pass_class_t spawnedPass = cmpUnitMotion->GetPassabilityClass();
CmpPtr<ICmpPathfinder> cmpPathfinder(GetSimContext(), SYSTEM_ENTITY);
if (!cmpPathfinder)
return error;
CFixedVector2D initialPos = cmpPosition->GetPosition2D();
entity_angle_t initialAngle = cmpPosition->GetRotation().Y;
// Max spawning distance in tiles
const i32 maxSpawningDistance = 4;
if (m_Shape == CIRCLE)
{
// Expand outwards from foundation
for (i32 dist = 0; dist <= maxSpawningDistance; ++dist)
{
// The spawn point should be far enough from this footprint to fit the unit, plus a little gap
entity_pos_t clearance = spawnedRadius + entity_pos_t::FromInt(2 + (int)TERRAIN_TILE_SIZE*dist);
entity_pos_t radius = m_Size0 + clearance;
// Try equally-spaced points around the circle in alternating directions, starting from the front
const i32 numPoints = 31 + 2*dist;
for (i32 i = 0; i < (numPoints+1)/2; i = (i > 0 ? -i : 1-i)) // [0, +1, -1, +2, -2, ... (np-1)/2, -(np-1)/2]
{
entity_angle_t angle = initialAngle + (entity_angle_t::Pi()*2).Multiply(entity_angle_t::FromInt(i)/(int)numPoints);
fixed s, c;
sincos_approx(angle, s, c);
CFixedVector3D pos (initialPos.X + s.Multiply(radius), fixed::Zero(), initialPos.Y + c.Multiply(radius));
SkipTagObstructionFilter filter(spawnedTag); // ignore collisions with the spawned entity
if (cmpPathfinder->CheckUnitPlacement(filter, pos.X, pos.Z, spawnedRadius, spawnedPass) == ICmpObstruction::FOUNDATION_CHECK_SUCCESS)
return pos; // this position is okay, so return it
}
}
}
else
{
fixed s, c;
sincos_approx(initialAngle, s, c);
// Expand outwards from foundation
for (i32 dist = 0; dist <= maxSpawningDistance; ++dist)
{
// The spawn point should be far enough from this footprint to fit the unit, plus a little gap
entity_pos_t clearance = spawnedRadius + entity_pos_t::FromInt(2 + (int)TERRAIN_TILE_SIZE*dist);
for (i32 edge = 0; edge < 4; ++edge)
{
// Try equally-spaced points along the edge in alternating directions, starting from the middle
const i32 numPoints = 9 + 2*dist;
// Compute the direction and length of the current edge
CFixedVector2D dir;
fixed sx, sy;
switch (edge)
{
case 0:
dir = CFixedVector2D(c, -s);
sx = m_Size0;
sy = m_Size1;
break;
case 1:
dir = CFixedVector2D(-s, -c);
sx = m_Size1;
sy = m_Size0;
break;
case 2:
dir = CFixedVector2D(s, c);
sx = m_Size1;
sy = m_Size0;
break;
case 3:
dir = CFixedVector2D(-c, s);
sx = m_Size0;
sy = m_Size1;
break;
}
CFixedVector2D center = initialPos - dir.Perpendicular().Multiply(sy/2 + clearance);
dir = dir.Multiply((sx + clearance*2) / (int)(numPoints-1));
for (i32 i = 0; i < (numPoints+1)/2; i = (i > 0 ? -i : 1-i)) // [0, +1, -1, +2, -2, ... (np-1)/2, -(np-1)/2]
{
CFixedVector2D pos (center + dir*i);
SkipTagObstructionFilter filter(spawnedTag); // ignore collisions with the spawned entity
if (cmpPathfinder->CheckUnitPlacement(filter, pos.X, pos.Y, spawnedRadius, spawnedPass) == ICmpObstruction::FOUNDATION_CHECK_SUCCESS)
return CFixedVector3D(pos.X, fixed::Zero(), pos.Y); // this position is okay, so return it
}
}
}
}
return error;
}
CFixedVector2D Geometry::NearestPointOnSquare(const CFixedVector2D& point, const CFixedVector2D& u, const CFixedVector2D& v, const CFixedVector2D& halfSize)
{
/*
* Relative to its own coordinate system, we have a square like:
*
* A : : C
* : :
* - - #### B #### - -
* #\ /#
* # \ / #
* D --0-- E v
* # / \ # ^
* #/ \# |
* - - #### G #### - - -->u
* : :
* F : : H
*
* where 0 is the center, u and v are unit axes,
* and the square is hw*2 by hh*2 units in size.
*
* Points in the BDEG regions are nearest to the corresponding edge.
* Points in the ACFH regions are nearest to the corresponding corner.
*
* So we just need to check all of the regions to work out which calculations to apply.
*
*/
// du, dv are the location of the point in the square's coordinate system
fixed du = point.Dot(u);
fixed dv = point.Dot(v);
fixed hw = halfSize.X;
fixed hh = halfSize.Y;
if (-hw < du && du < hw) // regions B, G; or regions D, E inside the square
{
if (-hh < dv && dv < hh && (du.Absolute() - hw).Absolute() < (dv.Absolute() - hh).Absolute()) // regions D, E
{
if (du >= fixed::Zero()) // E
return u.Multiply(hw) + v.Multiply(dv);
else // D
return -u.Multiply(hw) + v.Multiply(dv);
}
else // B, G
{
if (dv >= fixed::Zero()) // B
return v.Multiply(hh) + u.Multiply(du);
else // G
return -v.Multiply(hh) + u.Multiply(du);
}
}
else if (-hh < dv && dv < hh) // regions D, E outside the square
{
if (du >= fixed::Zero()) // E
return u.Multiply(hw) + v.Multiply(dv);
else // D
return -u.Multiply(hw) + v.Multiply(dv);
}
else // regions A, C, F, H
{
CFixedVector2D corner;
if (du < fixed::Zero()) // A, F
corner -= u.Multiply(hw);
else // C, H
corner += u.Multiply(hw);
if (dv < fixed::Zero()) // F, H
corner -= v.Multiply(hh);
else // A, C
corner += v.Multiply(hh);
return corner;
}
}