DirectX::BoundingOrientedBox GetBoundsInOrientedSpace(_In_ bool findTightestBounds, _In_ function<bool(XMFLOAT3*)> vertGenerator)
{
// we find tight bounds by
// 1. find the convex hull
// 2. rotating calipers to find the ideal bounding box - http://en.wikipedia.org/wiki/Rotating_calipers
// The idea behind rotating calipers is that we keep track of some extreme vertices, and slowly rotate our coordinate frame.
// As we rotate, a vertex may no-longer be extreme in the new rotated coordinate frame, so we increment the index to the next vertex
// in the convex hull that is now extreme.
float zmin = FLT_MAX, zmax = -FLT_MAX;
auto convexHull = FindConvexHull([&](XMFLOAT2 *planarVert, UINT32 *index) -> bool
{
*index = 0; // we dont' care about the index here - only useful when exposing the convex hull directly
XMFLOAT3 vert;
bool ret = vertGenerator(&vert);
if (ret)
{
if (vert.z < zmin)
{
zmin = vert.z;
}
if (vert.z > zmax)
{
zmax = vert.z;
}
}
*planarVert = { vert.x, vert.y };
return ret;
});
// first we need to set up the calipers - extreme vertices that we will incrementally update as we rotate
XMFLOAT2 maxv = convexHull[0].first;
XMFLOAT2 minv = convexHull[0].first;
struct RotatedBoundingBox
{
UINT32 maxx, maxy, minx, miny; // these represent the indices of the max/min x and y coordinates in a rotated coordated frame.
float area;
float minwidth;
float angle;
};
// find the initial orientation's bounds:
RotatedBoundingBox best = { 0, 0, 0, 0, FLT_MAX, FLT_MAX, XM_2PI };
for (UINT32 i = 1; i < convexHull.size(); ++i)
{
const auto vertex = convexHull[i].first;
if (vertex.x > maxv.x)
{
maxv.x = vertex.x;
best.maxx = i;
}
else if (vertex.x < minv.x)
{
minv.x = vertex.x;
best.minx = i;
}
if (vertex.y > maxv.y)
{
maxv.y = vertex.y;
best.maxy = i;
}
else if (vertex.y < minv.y)
{
minv.y = vertex.y;
best.miny = i;
}
}
best.angle = 0;
best.area = (maxv.x - minv.x) * (maxv.y - minv.y);
best.minwidth = min(maxv.x - minv.x, maxv.y - minv.y);
ASSERT(best.minx != best.maxx); // xmin and xmax indices should never be the same
ASSERT(best.miny != best.maxy);
ASSERT(best.minx <= best.maxy); // our vertices should be located around the convex hull xmin->ymax->xmax->ymin
ASSERT(best.maxy <= best.maxx);
ASSERT(best.maxx <= best.miny || best.minx == best.miny);
ASSERT(best.miny <= best.minx + convexHull.size());
ASSERT(best.minx <= convexHull.size()); // all of the indices should be in the convex hull
ASSERT(best.maxx <= convexHull.size());
ASSERT(best.miny <= convexHull.size());
ASSERT(best.maxy <= convexHull.size());
ASSERT(best.minx == 0); // we expect minx to be the first vertex in the convex hull
// Helper to calculate the rotation if we move from the given vertex to the next vertex in the convex hull
auto getDeltaVectorForIndex = [&](UINT32 vert)
{
// return the delta between the given vertex and the subsequent vertex, so we can determine the angle our bounding box
// would have to rotate to be parallel with this edge
auto start = convexHull[vert % convexHull.size()].first;
auto next = convexHull[(vert + 1) % convexHull.size()].first;
ASSERT(start.x != next.x || start.y != next.y);
return XMFLOAT2({ next.x - start.x, next.y - start.y });
};
// once we have the extreme vertices, we slowly rotate our coordinate system and adjust them
// we rotate in such a way that only one extreme vertex changes at a time
float angle = 0;
RotatedBoundingBox current = best;
BoundingOrientedBox bestBoxInPlaneSpace;
bestBoxInPlaneSpace.Center = { (maxv.x + minv.x) / 2, (maxv.y + minv.y) / 2, (zmax + zmin) / 2 };
bestBoxInPlaneSpace.Extents = { (maxv.x - minv.x) / 2, (maxv.y - minv.y) / 2, (zmax - zmin) / 2 };
bestBoxInPlaneSpace.Orientation = { 0, 0, 0, 1 };
if (findTightestBounds)
{
RotatedBoundingBox initial = best;
// The tightest bounding box will share a side with the convex hull. We start with a candidate bounding box oriented along
// the x/y axes and iterate through all orientations where the box is aligned with an edge of the convex hull. The maximum possible rotations
// we need to consider is convexHull.size(), which would be a rotation of 90 degrees.
// Each iteration through the loop, we pick the vertex from our extreme vertices that has the smallest incremental rotation along its outgoing edge.
// A neat trick is that the other extreme vertices remain extreme in the new rotated orientation.
while (angle <= XM_PIDIV2 + ROTATING_CALIPERS_EPSILON &&
current.minx <= initial.maxy &&
current.maxy <= initial.maxx &&
current.maxx <= initial.miny &&
current.miny <= convexHull.size())
{
const auto vectForXmin = getDeltaVectorForIndex(current.minx);
const auto vectForXmax = getDeltaVectorForIndex(current.maxx);
const auto vectForYmin = getDeltaVectorForIndex(current.miny);
const auto vectForYmax = getDeltaVectorForIndex(current.maxy);
UINT32* boundIndices[4] = { ¤t.minx, ¤t.maxx, ¤t.miny, ¤t.maxy };
float angles[4] = {
atan2(vectForXmin.x, vectForXmin.y),
atan2(-vectForXmax.x, -vectForXmax.y),
atan2(vectForYmin.y, -vectForYmin.x),
atan2(-vectForYmax.y, vectForYmax.x) };
int index = 0;
float minAngle = XM_PI * 4 + angle;
for (int i = 0; i < 4; ++i)
{
if (angles[i] > -ROTATING_CALIPERS_EPSILON && angles[i] < 0)
{
// the vector between vertices are horizontal/vertical, so angle is close to 0, treat it as zero
// this can only occur with a rounding error
angles[i] = 0;
}
else if (angles[i] < 0)
{
angles[i] += XM_PI * 2;
}
if (angles[i] < minAngle)
{
minAngle = angles[i];
index = i;
}
}
*(boundIndices[index]) = ((*(boundIndices[index])) + 1);
ASSERT(current.minx <= current.maxy); // we should remain ordering of vertices xmin->ymax->xmax->ymin as we rotate
ASSERT(current.maxy <= current.maxx);
ASSERT(current.maxx <= current.miny || best.minx == best.miny);
ASSERT(current.miny <= current.minx + convexHull.size());
ASSERT(current.minx != current.maxx); // and we shouldn't ever have min and max indices equal
ASSERT(current.miny != current.maxy);
// now update our box:
angle = minAngle;
current.angle = minAngle;
if (angle < XM_PIDIV2 + ROTATING_CALIPERS_EPSILON)
{
XMVECTOR vertsInRotatedPlaneSpace[4];
const XMMATRIX rotationTransform = XMMatrixRotationZ(angle);
for (int i = 0; i < 4; ++i)
{
vertsInRotatedPlaneSpace[i] = XMVector3TransformCoord(XMLoadFloat2(&convexHull[(*(boundIndices[i])) % convexHull.size()].first), rotationTransform);
}
BoundingOrientedBox xmBoundsInPlaneSpace;
xmBoundsInPlaneSpace.Center = { XMVectorGetX(vertsInRotatedPlaneSpace[0] + vertsInRotatedPlaneSpace[1]) / 2, XMVectorGetY(vertsInRotatedPlaneSpace[2] + vertsInRotatedPlaneSpace[3]) / 2, (zmax + zmin) / 2 };
xmBoundsInPlaneSpace.Extents = { XMVectorGetX(vertsInRotatedPlaneSpace[1] - vertsInRotatedPlaneSpace[0]) / 2, XMVectorGetY(vertsInRotatedPlaneSpace[3] - vertsInRotatedPlaneSpace[2]) / 2, (zmax - zmin) / 2 };
xmBoundsInPlaneSpace.Orientation = { 0, 0, 0, 1 };
xmBoundsInPlaneSpace.Transform(xmBoundsInPlaneSpace, XMMatrixTranspose(rotationTransform)); // rotate back to plane space from rotated plane space
const XMFLOAT2 size = { xmBoundsInPlaneSpace.Extents.x * 2, xmBoundsInPlaneSpace.Extents.y * 2 };
current.area = size.x * size.y;
current.minwidth = min(size.x, size.y);
if (current.area < best.area || (current.area == best.area && current.minwidth < best.minwidth))
{
best = current;
bestBoxInPlaneSpace = xmBoundsInPlaneSpace;
}
}
}
}
return bestBoxInPlaneSpace;
}
// recursively render meshes for all nodes
// lambda-free version
bool CompoundMesh::render( ID3D11DeviceContext *deviceContext, VanillaShaderClass *shader, DirectX::CXMMATRIX worldMatrix, DirectX::CXMMATRIX viewMatrix, DirectX::CXMMATRIX projectionMatrix, std::vector<Light> &lights, bool orthoProjection /*= false*/, double animationTick /*= 1.0*/, CompoundMeshNode *node /*= nullptr*/, DirectX::CXMMATRIX parentNodeTransform /*= XMMatrixIdentity()*/ )
{
if (!node)
{
// top-level invocation; do some initialization and culling
node = m_root.get();
if (m_animation.loaded())
{
double ticksPerSec = m_aiScene->mAnimations[0]->mTicksPerSecond;
if (ticksPerSec <= 0) ticksPerSec = 24;
animationTick *= ticksPerSec;
animationTick += 1; // time starts at 0 but ticks, alas, at 1?
while (animationTick > m_animation.maxTick) animationTick -= m_animation.maxTick;
updateNodeTransforms(animationTick);
}
// clip to view frustum
BoundingSphere bSphere(m_bSphere);
bSphere.Transform(bSphere, worldMatrix);
//BoundingOrientedBox bBox;
//m_bBox.Transform(bBox, worldMatrix);
if (!orthoProjection)
{
BoundingFrustum frustum(projectionMatrix); // TODO this should be moved somewhere higher up if the engine ever becomes CPU-bound
XMStoreFloat4(&frustum.Orientation, XMVectorSet(0, 0, 0, 1)); // identity quaternion
frustum.Transform(frustum, XMMatrixInverse(nullptr, viewMatrix)); // move the frustum as though it was an object within the world; probably slow?
if (!DirectX::Internal::XMQuaternionIsUnit(XMLoadFloat4(&frustum.Orientation)))
{
cerr << "Bad frustum quaternion! :( " << XMLoadFloat4(&frustum.Orientation) << endl;
XMStoreFloat4(&frustum.Orientation, XMVectorSet(0, 0, 0, 1));
}
try
{
if (!frustum.Intersects(bSphere)) return true;
} catch (exception *e)
{
cerr << e->what() << endl;
}
} else
{
// make a bounding box from the orthographic projection matrix (is this weird? perhaps it's weird.)
XMMATRIX unproj = XMMatrixInverse(nullptr, projectionMatrix);
float x = unproj.r[0].m128_f32[0]; // half the width; for now, assuming projection centered at origin
float y = unproj.r[1].m128_f32[1]; // half the height
float near_plane = unproj.r[3].m128_f32[2];
float far_plane = unproj.r[2].m128_f32[2] + near_plane;
XMFLOAT3 points[2];
points[0].x = -x;
points[0].y = -y;
points[0].z = near_plane;
points[1].x = x;
points[1].y = y;
points[1].z = max(far_plane,10000); // /fp:fast workaround ಠ_ಠ
//points[1].z = far_plane;
// XXX XXX XXX Something about this code fails with /fp:fast XXX XXX XXX
// one workaround is to set far_plane to 10000; we're probably not culling based on distance anyway so no harm done, at least?
// another is, of course, to set /fp:precise ... this costs several FPS on the i7 laptop with the double-torus test scene!
BoundingOrientedBox viewBox;
viewBox.CreateFromPoints(viewBox, 2, points, sizeof(XMFLOAT3));
XMStoreFloat4(&viewBox.Orientation, XMVectorSet(0, 0, 0, 1)); // identity quaternion... strange that Orientation would be uninitialized though
viewBox.Transform(viewBox, XMMatrixInverse(nullptr, viewMatrix));
if (!DirectX::Internal::XMQuaternionIsUnit(XMLoadFloat4(&viewBox.Orientation)))
{
cerr << "Bad viewBox quaternion! :( " << XMLoadFloat4(&viewBox.Orientation) << endl;
XMStoreFloat4(&viewBox.Orientation, XMVectorSet(0, 0, 0, 1));
}
// clip to viewbox
try
{
if (!viewBox.Intersects(bSphere)) return true;
} catch (exception *e)
{
cerr << e->what() << endl;
}
}
// tell the vertex shader about the wonderful animation buffer we have for it:
if (m_animation.loaded())
{
m_animation.updateCurrentBoneKeys(deviceContext, animationTick);
}
}
for (auto mesh = node->meshes.begin(), end = node->meshes.end(); mesh != end; ++mesh)
{
if (mesh->m_indexBuffer == nullptr || mesh->m_vertexBuffer == nullptr || !mesh->getIndexCount())
{
cerr << "strange, empty mesh";
continue;
}
mesh->setBuffers(deviceContext); // point the GPU at the right geometry data
SimpleMesh::Material &mat = mesh->m_material;
bool useNormalMap = mat.normalMap.getTexture() ? true : false;
bool useSpecularMap = mat.specularMap.getTexture() ? true : false;
if (!shader->SetPSMaterial(deviceContext, mat.ambient, mat.diffuse, mat.shininess, mat.specular, useNormalMap, useSpecularMap))
{
return false;
}
XMFLOAT4X4 *offsetMatrix = nullptr;
if (m_animation.loaded())
{
m_animation.updateBoneTransforms(deviceContext, animationTick, mesh->m_OffsetMatrix, mesh->m_name,
[&](std::string nodeName)
{
return getNodeGlobalTransform(nodeName);
}
);
}
XMMATRIX finalWorldMatrix;
if (!m_animation.loaded() && node->name.size() == 0)
{
finalWorldMatrix = worldMatrix;
} else
{
finalWorldMatrix = XMMatrixMultiply(getNodeGlobalTransform(node->name), worldMatrix);
}
if (!shader->Render(deviceContext, mesh->getIndexCount(), finalWorldMatrix, viewMatrix, projectionMatrix, mesh->m_material.normalMap.getTexture(), mesh->m_material.specularMap.getTexture(), &lights, mesh->m_material.diffuseTexture.getTexture(), 1, true, m_animation.loaded() ? animationTick : -1))
{
return false;
}
}
for (auto i : node->children)
{
if (!render(deviceContext, shader, worldMatrix, viewMatrix, projectionMatrix, lights, orthoProjection, animationTick, i.get(), XMMatrixIdentity())) return false;
}
return true;
}