986 lines
		
	
	
	
		
			35 KiB
		
	
	
	
		
			C++
		
	
	
	
	
	
			
		
		
	
	
			986 lines
		
	
	
	
		
			35 KiB
		
	
	
	
		
			C++
		
	
	
	
	
	
| // Copyright 2009-2021 Intel Corporation
 | |
| // SPDX-License-Identifier: Apache-2.0
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| 
 | |
| #include "scene_subdiv_mesh.h"
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| #include "scene.h"
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| #include "../subdiv/patch_eval.h"
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| #include "../subdiv/patch_eval_simd.h"
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| 
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| #include "../../common/algorithms/parallel_map.h"
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| #include "../../common/algorithms/parallel_set.h"
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| #include "../../common/algorithms/parallel_sort.h"
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| #include "../../common/algorithms/parallel_prefix_sum.h"
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| #include "../../common/algorithms/parallel_for.h"
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| 
 | |
| /*! maximum number of user vertex buffers for subdivision surfaces */
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| #define RTC_MAX_USER_VERTEX_BUFFERS 65536
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| 
 | |
| namespace embree
 | |
| {
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| #if defined(EMBREE_LOWEST_ISA)
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| 
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|   struct VertexCreaseMap {
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|     parallel_map<uint32_t,float> vertexCreaseMap;
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|   };
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|   struct EdgeCreaseMap {
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|     parallel_map<uint64_t,float> edgeCreaseMap;
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|   };
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|   struct HoleSet{
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|     parallel_set<uint32_t> holeSet;
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|   };
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| 
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|   SubdivMesh::SubdivMesh (Device* device)
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|     : Geometry(device,GTY_SUBDIV_MESH,0,1), 
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|       displFunc(nullptr),
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|       tessellationRate(2.0f),
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|       numHalfEdges(0),
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|       faceStartEdge(device,0),
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|       halfEdgeFace(device,0),
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|       holeSet(new HoleSet),
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|       invalid_face(device,0),
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|       vertexCreaseMap(new VertexCreaseMap),
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|       edgeCreaseMap(new EdgeCreaseMap),
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|       commitCounter(0)
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|   {
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|     
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|     vertices.resize(numTimeSteps);
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|     vertex_buffer_tags.resize(numTimeSteps);
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|     topology.resize(1);
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|     topology[0] = Topology(this);
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|   }
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| 
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|   SubdivMesh::~SubdivMesh() {}
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| 
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|   void SubdivMesh::addElementsToCount (GeometryCounts & counts) const
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|   {
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|     if (numTimeSteps == 1) counts.numSubdivPatches += numPrimitives;
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|     else                   counts.numMBSubdivPatches += numPrimitives;
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|   }
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| 
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|   void SubdivMesh::setMask (unsigned mask) 
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|   {
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|     this->mask = mask; 
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|     Geometry::update();
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|   }
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| 
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|   void SubdivMesh::setSubdivisionMode (unsigned topologyID, RTCSubdivisionMode mode)
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|   {
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|     if (topologyID >= topology.size())
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|       throw_RTCError(RTC_ERROR_INVALID_OPERATION,"invalid topology ID");
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|     topology[topologyID].setSubdivisionMode(mode);
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|     Geometry::update();
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|   }
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| 
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|   void SubdivMesh::setVertexAttributeTopology(unsigned int vertexAttribID, unsigned int topologyID)
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|   {
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|     if (vertexAttribID < vertexAttribs.size()){
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|       if (topologyID < topology.size()) {
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|         if ((unsigned)vertexAttribs[vertexAttribID].userData != topologyID) {
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|           vertexAttribs[vertexAttribID].userData = topologyID;
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|           commitCounter++; // triggers recalculation of cached interpolation data
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|         }
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|       } else {
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid topology specified");
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|       }
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|     } else {
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|       throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex attribute specified");
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|     }
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|   }
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| 
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|   void SubdivMesh::setNumTimeSteps (unsigned int numTimeSteps)
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|   {
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|     vertices.resize(numTimeSteps);
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|     vertex_buffer_tags.resize(numTimeSteps);
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|     Geometry::setNumTimeSteps(numTimeSteps);
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|   }
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| 
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|   void SubdivMesh::setVertexAttributeCount (unsigned int N)
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|   {
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|     vertexAttribs.resize(N);
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|     vertex_attrib_buffer_tags.resize(N);
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|     Geometry::update();
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|   }
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| 
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|   void SubdivMesh::setTopologyCount (unsigned int N)
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|   {
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|     if (N == 0)
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|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT,"at least one topology has to exist")
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|         
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|     size_t begin = topology.size();
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|     topology.resize(N);
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|     for (size_t i = begin; i < topology.size(); i++)
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|       topology[i] = Topology(this);
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|   }
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|   
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|   void SubdivMesh::setBuffer(RTCBufferType type, unsigned int slot, RTCFormat format, const Ref<Buffer>& buffer, size_t offset, size_t stride, unsigned int num)
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|   { 
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|     /* verify that all accesses are 4 bytes aligned */
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|     if (((size_t(buffer->getPtr()) + offset) & 0x3) || (stride & 0x3))
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|       throw_RTCError(RTC_ERROR_INVALID_OPERATION, "data must be 4 bytes aligned");
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| 
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|     if (type != RTC_BUFFER_TYPE_LEVEL)
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|       commitCounter++;
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| 
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|     if (type == RTC_BUFFER_TYPE_VERTEX)
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|     {
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|       if (format != RTC_FORMAT_FLOAT3)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex buffer format");
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| 
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|       if (slot >= vertices.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid vertex buffer slot");
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| 
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|       vertices[slot].set(buffer, offset, stride, num, format);
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|       vertices[slot].checkPadding16();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE)
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|     {
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|       if (format < RTC_FORMAT_FLOAT || format > RTC_FORMAT_FLOAT16)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex attribute buffer format");
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| 
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|       if (slot >= vertexAttribs.size())
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex attribute buffer slot");
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|       
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|       vertexAttribs[slot].set(buffer, offset, stride, num, format);
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|       vertexAttribs[slot].checkPadding16();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_FACE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_UINT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid face buffer format");
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| 
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|       faceVertices.set(buffer, offset, stride, num, format);
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|       setNumPrimitives(num);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_INDEX)
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|     {
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|       if (format != RTC_FORMAT_UINT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid face buffer format");
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| 
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|       if (slot >= topology.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid index buffer slot");
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| 
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|       topology[slot].vertexIndices.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_INDEX)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_UINT2)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid edge crease index buffer format");
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| 
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|       edge_creases.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_FLOAT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid edge crease weight buffer format");
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| 
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|       edge_crease_weights.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_INDEX)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_UINT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex crease index buffer format");
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| 
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|       vertex_creases.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_FLOAT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid vertex crease weight buffer format");
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| 
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|       vertex_crease_weights.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_HOLE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_UINT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid hole buffer format");
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| 
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|       holes.set(buffer, offset, stride, num, format);
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|     }
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|     else if (type == RTC_BUFFER_TYPE_LEVEL)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       if (format != RTC_FORMAT_FLOAT)
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|         throw_RTCError(RTC_ERROR_INVALID_OPERATION, "invalid level buffer format");
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| 
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|       levels.set(buffer, offset, stride, num, format);
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|     }
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|     else
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|     {
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|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT,"unknown buffer type");
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|     }
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|   }
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| 
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|   void* SubdivMesh::getBuffer(RTCBufferType type, unsigned int slot)
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|   {
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|     if (type == RTC_BUFFER_TYPE_VERTEX)
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|     {
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|       if (slot >= vertices.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return vertices[slot].getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE)
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|     {
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|       if (slot >= vertexAttribs.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return vertexAttribs[slot].getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_FACE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return faceVertices.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_INDEX)
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|     {
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|       if (slot >= topology.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return topology[slot].vertexIndices.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_INDEX)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return edge_creases.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return edge_crease_weights.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_INDEX)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return vertex_creases.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return vertex_crease_weights.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_HOLE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return holes.getPtr();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_LEVEL)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       return levels.getPtr();
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|     }
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|     else
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|     {
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|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "unknown buffer type");
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|       return nullptr;
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|     }
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|   }
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| 
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|   void SubdivMesh::updateBuffer(RTCBufferType type, unsigned int slot)
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|   {
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|     if (type != RTC_BUFFER_TYPE_LEVEL)
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|       commitCounter++;
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| 
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|     if (type == RTC_BUFFER_TYPE_VERTEX)
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|     {
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|       if (slot >= vertices.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       vertices[slot].setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE)
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|     {
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|       if (slot >= vertexAttribs.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       vertexAttribs[slot].setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_FACE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       faceVertices.setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_INDEX)
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|     {
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|       if (slot >= topology.size())
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       topology[slot].vertexIndices.setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_INDEX)
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|     {
 | |
|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       edge_creases.setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_EDGE_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       edge_crease_weights.setModified();
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|     }
 | |
|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_INDEX)
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|     {
 | |
|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       vertex_creases.setModified();
 | |
|     }
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|     else if (type == RTC_BUFFER_TYPE_VERTEX_CREASE_WEIGHT)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       vertex_crease_weights.setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_HOLE)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       holes.setModified();
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|     }
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|     else if (type == RTC_BUFFER_TYPE_LEVEL)
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|     {
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|       if (slot != 0)
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|         throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid buffer slot");
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|       levels.setModified();
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|     }
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|     else
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|     {
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|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "unknown buffer type");
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|     }
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| 
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|     Geometry::update();
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|   }
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| 
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|   void SubdivMesh::setDisplacementFunction (RTCDisplacementFunctionN func) 
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|   {
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|     this->displFunc = func;
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|   }
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| 
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|   void SubdivMesh::setTessellationRate(float N)
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|   {
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|     tessellationRate = N;
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|     levels.setModified();
 | |
|   }
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| 
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|   __forceinline uint64_t pair64(unsigned int x, unsigned int y) 
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|   {
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|     if (x<y) std::swap(x,y);
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|     return (((uint64_t)x) << 32) | (uint64_t)y;
 | |
|   }
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| 
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|   SubdivMesh::Topology::Topology(SubdivMesh* mesh)
 | |
|     : mesh(mesh), subdiv_mode(RTC_SUBDIVISION_MODE_SMOOTH_BOUNDARY), halfEdges(mesh->device,0)
 | |
|   {
 | |
|   }
 | |
|   
 | |
|   void SubdivMesh::Topology::setSubdivisionMode (RTCSubdivisionMode mode)
 | |
|   {
 | |
|     if (subdiv_mode == mode) return;
 | |
|     subdiv_mode = mode;
 | |
|     mesh->updateBuffer(RTC_BUFFER_TYPE_VERTEX_CREASE_WEIGHT, 0);
 | |
|   }
 | |
|   
 | |
|   void SubdivMesh::Topology::update () {
 | |
|     vertexIndices.setModified();
 | |
|   }
 | |
| 
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|   bool SubdivMesh::Topology::verify (size_t numVertices) 
 | |
|   {
 | |
|     size_t ofs = 0;
 | |
|     for (size_t i=0; i<mesh->size(); i++) 
 | |
|     {
 | |
|       int valence = mesh->faceVertices[i];
 | |
|       for (size_t j=ofs; j<ofs+valence; j++) 
 | |
|       {
 | |
|         if (j >= vertexIndices.size())
 | |
|           return false;
 | |
|           
 | |
|         if (vertexIndices[j] >= numVertices)
 | |
|           return false; 
 | |
|       }
 | |
|       ofs += valence;
 | |
|     }
 | |
|     return true;
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::Topology::calculateHalfEdges()
 | |
|   {
 | |
|     const size_t blockSize = 4096;
 | |
|     const size_t numEdges = mesh->numEdges();
 | |
|     const size_t numFaces = mesh->numFaces();
 | |
|     const size_t numHalfEdges = mesh->numHalfEdges;
 | |
| 
 | |
|     /* allocate temporary array */
 | |
|     halfEdges0.resize(numEdges);
 | |
|     halfEdges1.resize(numEdges);
 | |
| 
 | |
|     /* create all half edges */
 | |
|     parallel_for( size_t(0), numFaces, blockSize, [&](const range<size_t>& r) 
 | |
|     {
 | |
|       for (size_t f=r.begin(); f<r.end(); f++) 
 | |
|       {
 | |
| 	const unsigned N = mesh->faceVertices[f];
 | |
| 	const unsigned e = mesh->faceStartEdge[f];
 | |
| 
 | |
| 	for (unsigned de=0; de<N; de++)
 | |
| 	{
 | |
| 	  HalfEdge* edge = &halfEdges[e+de];
 | |
|           int nextOfs = (de == (N-1)) ? -int(N-1) : +1;
 | |
|           int prevOfs = (de ==     0) ? +int(N-1) : -1;
 | |
| 	  
 | |
| 	  const unsigned int startVertex = vertexIndices[e+de];
 | |
|           const unsigned int endVertex = vertexIndices[e+de+nextOfs]; 
 | |
| 	  const uint64_t key = SubdivMesh::Edge(startVertex,endVertex);
 | |
| 
 | |
|           /* we always have to use the geometry topology to lookup creases */
 | |
|           const unsigned int startVertex0 = mesh->topology[0].vertexIndices[e+de];
 | |
|           const unsigned int endVertex0 = mesh->topology[0].vertexIndices[e+de+nextOfs]; 
 | |
| 	  const uint64_t key0 = SubdivMesh::Edge(startVertex0,endVertex0);
 | |
| 	  
 | |
| 	  edge->vtx_index              = startVertex;
 | |
| 	  edge->next_half_edge_ofs     = nextOfs;
 | |
| 	  edge->prev_half_edge_ofs     = prevOfs;
 | |
| 	  edge->opposite_half_edge_ofs = 0;
 | |
| 	  edge->edge_crease_weight     = mesh->edgeCreaseMap->edgeCreaseMap.lookup(key0,0.0f);
 | |
| 	  edge->vertex_crease_weight   = mesh->vertexCreaseMap->vertexCreaseMap.lookup(startVertex0,0.0f);
 | |
| 	  edge->edge_level             = mesh->getEdgeLevel(e+de);
 | |
|           edge->patch_type             = HalfEdge::COMPLEX_PATCH; // type gets updated below
 | |
|           edge->vertex_type            = HalfEdge::REGULAR_VERTEX;
 | |
| 
 | |
|           if (unlikely(mesh->holeSet->holeSet.lookup(unsigned(f)))) 
 | |
| 	    halfEdges1[e+de] = SubdivMesh::KeyHalfEdge(std::numeric_limits<uint64_t>::max(),edge);
 | |
| 	  else
 | |
| 	    halfEdges1[e+de] = SubdivMesh::KeyHalfEdge(key,edge);
 | |
| 	}
 | |
|       }
 | |
|     });
 | |
| 
 | |
|     /* sort half edges to find adjacent edges */
 | |
|     radix_sort_u64(halfEdges1.data(),halfEdges0.data(),numHalfEdges);
 | |
| 
 | |
|     /* link all adjacent pairs of edges */
 | |
|     parallel_for( size_t(0), numHalfEdges, blockSize, [&](const range<size_t>& r) 
 | |
|     {
 | |
|       /* skip if start of adjacent edges was not in our range */
 | |
|       size_t e=r.begin();
 | |
|       if (e != 0 && (halfEdges1[e].key == halfEdges1[e-1].key)) {
 | |
| 	const uint64_t key = halfEdges1[e].key;
 | |
| 	while (e<r.end() && halfEdges1[e].key == key) e++;
 | |
|       }
 | |
| 
 | |
|       /* process all adjacent edges starting in our range */
 | |
|       while (e<r.end())
 | |
|       {
 | |
| 	const uint64_t key = halfEdges1[e].key;
 | |
| 	if (key == std::numeric_limits<uint64_t>::max()) break;
 | |
| 	size_t N=1; while (e+N<numHalfEdges && halfEdges1[e+N].key == key) N++;
 | |
| 
 | |
|         /* border edges are identified by not having an opposite edge set */
 | |
| 	if (N == 1) {
 | |
|           halfEdges1[e].edge->edge_crease_weight = float(inf);
 | |
| 	}
 | |
| 
 | |
|         /* standard edge shared between two faces */
 | |
|         else if (N == 2)
 | |
|         {
 | |
|           /* create edge crease if winding order mismatches between neighboring patches */
 | |
|           if (halfEdges1[e+0].edge->next()->vtx_index != halfEdges1[e+1].edge->vtx_index)
 | |
|           {
 | |
|             halfEdges1[e+0].edge->edge_crease_weight = float(inf);
 | |
|             halfEdges1[e+1].edge->edge_crease_weight = float(inf);
 | |
|           }
 | |
|           /* otherwise mark edges as opposites of each other */
 | |
|           else {
 | |
|             halfEdges1[e+0].edge->setOpposite(halfEdges1[e+1].edge);
 | |
|             halfEdges1[e+1].edge->setOpposite(halfEdges1[e+0].edge);
 | |
|           }
 | |
| 	}
 | |
| 
 | |
|         /* non-manifold geometry is handled by keeping vertices fixed during subdivision */
 | |
|         else {
 | |
| 	  for (size_t i=0; i<N; i++) {
 | |
| 	    halfEdges1[e+i].edge->vertex_crease_weight = inf;
 | |
|             halfEdges1[e+i].edge->vertex_type = HalfEdge::NON_MANIFOLD_EDGE_VERTEX;
 | |
|             halfEdges1[e+i].edge->edge_crease_weight = inf;
 | |
| 
 | |
| 	    halfEdges1[e+i].edge->next()->vertex_crease_weight = inf;
 | |
|             halfEdges1[e+i].edge->next()->vertex_type = HalfEdge::NON_MANIFOLD_EDGE_VERTEX;
 | |
|             halfEdges1[e+i].edge->next()->edge_crease_weight = inf;
 | |
| 	  }
 | |
| 	}
 | |
| 	e+=N;
 | |
|       }
 | |
|     });
 | |
| 
 | |
|     /* set subdivision mode and calculate patch types */
 | |
|     parallel_for( size_t(0), numFaces, blockSize, [&](const range<size_t>& r) 
 | |
|     {
 | |
|       for (size_t f=r.begin(); f<r.end(); f++) 
 | |
|       {
 | |
|         HalfEdge* edge = &halfEdges[mesh->faceStartEdge[f]];
 | |
| 
 | |
|         /* for vertex topology we also test if vertices are valid */
 | |
|         if (this == &mesh->topology[0])
 | |
|         {
 | |
|           /* calculate if face is valid */
 | |
|           for (size_t t=0; t<mesh->numTimeSteps; t++)
 | |
|             mesh->invalidFace(f,t) = !edge->valid(mesh->vertices[t]) || mesh->holeSet->holeSet.lookup(unsigned(f));
 | |
|         }
 | |
| 
 | |
|         /* pin some edges and vertices */
 | |
|         for (size_t i=0; i<mesh->faceVertices[f]; i++) 
 | |
|         {
 | |
|           /* pin corner vertices when requested by user */
 | |
|           if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_CORNERS && edge[i].isCorner())
 | |
|             edge[i].vertex_crease_weight = float(inf);
 | |
|           
 | |
|           /* pin all border vertices when requested by user */
 | |
|           else if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_BOUNDARY && edge[i].vertexHasBorder()) 
 | |
|             edge[i].vertex_crease_weight = float(inf);
 | |
| 
 | |
|           /* pin all edges and vertices when requested by user */
 | |
|           else if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_ALL) {
 | |
|             edge[i].edge_crease_weight = float(inf);
 | |
|             edge[i].vertex_crease_weight = float(inf);
 | |
|           }
 | |
|         }
 | |
| 
 | |
|         /* we have to calculate patch_type last! */
 | |
|         HalfEdge::PatchType patch_type = edge->patchType();
 | |
|         for (size_t i=0; i<mesh->faceVertices[f]; i++) 
 | |
|           edge[i].patch_type = patch_type;
 | |
|       }
 | |
|     });
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::Topology::updateHalfEdges()
 | |
|   {
 | |
|     /* we always use the geometry topology to lookup creases */
 | |
|     mvector<HalfEdge>& halfEdgesGeom = mesh->topology[0].halfEdges;
 | |
| 
 | |
|     /* assume we do no longer recalculate in the future and clear these arrays */
 | |
|     halfEdges0.clear();
 | |
|     halfEdges1.clear();
 | |
| 
 | |
|     /* calculate which data to update */
 | |
|     const bool updateEdgeCreases   = mesh->topology[0].vertexIndices.isLocalModified() || mesh->edge_creases.isLocalModified()   || mesh->edge_crease_weights.isLocalModified();
 | |
|     const bool updateVertexCreases = mesh->topology[0].vertexIndices.isLocalModified() || mesh->vertex_creases.isLocalModified() || mesh->vertex_crease_weights.isLocalModified(); 
 | |
|     const bool updateLevels = mesh->levels.isLocalModified();
 | |
| 
 | |
|     /* parallel loop over all half edges */
 | |
|     parallel_for( size_t(0), mesh->numHalfEdges, size_t(4096), [&](const range<size_t>& r) 
 | |
|     {
 | |
|       for (size_t i=r.begin(); i!=r.end(); i++)
 | |
|       {
 | |
| 	HalfEdge& edge = halfEdges[i];
 | |
| 
 | |
| 	if (updateLevels)
 | |
| 	  edge.edge_level = mesh->getEdgeLevel(i); 
 | |
|         
 | |
| 	if (updateEdgeCreases) {
 | |
| 	  if (edge.hasOpposite()) // leave weight at inf for borders
 | |
|             edge.edge_crease_weight = mesh->edgeCreaseMap->edgeCreaseMap.lookup((uint64_t)halfEdgesGeom[i].getEdge(),0.0f);
 | |
| 	}
 | |
|         
 | |
|         /* we only use user specified vertex_crease_weight if the vertex is manifold */
 | |
|         if (updateVertexCreases && edge.vertex_type != HalfEdge::NON_MANIFOLD_EDGE_VERTEX) 
 | |
|         {
 | |
| 	  edge.vertex_crease_weight = mesh->vertexCreaseMap->vertexCreaseMap.lookup(halfEdgesGeom[i].vtx_index,0.0f);
 | |
| 
 | |
|           /* pin corner vertices when requested by user */
 | |
|           if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_CORNERS && edge.isCorner())
 | |
|             edge.vertex_crease_weight = float(inf);
 | |
|           
 | |
|           /* pin all border vertices when requested by user */
 | |
|           else if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_BOUNDARY && edge.vertexHasBorder()) 
 | |
|             edge.vertex_crease_weight = float(inf);
 | |
| 
 | |
|           /* pin every vertex when requested by user */
 | |
|           else if (subdiv_mode == RTC_SUBDIVISION_MODE_PIN_ALL) {
 | |
|             edge.edge_crease_weight = float(inf);
 | |
|             edge.vertex_crease_weight = float(inf);
 | |
|           }
 | |
|         }
 | |
| 
 | |
|         /* update patch type */
 | |
|         if (updateEdgeCreases || updateVertexCreases) {
 | |
|           edge.patch_type = edge.patchType();
 | |
|         }
 | |
|       }
 | |
|     });
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::Topology::initializeHalfEdgeStructures ()
 | |
|   {
 | |
|     /* if vertex indices not set we ignore this topology */
 | |
|     if (!vertexIndices)
 | |
|       return;
 | |
| 
 | |
|     /* allocate half edge array */
 | |
|     halfEdges.resize(mesh->numEdges());
 | |
| 
 | |
|     /* check if we have to recalculate the half edges */
 | |
|     bool recalculate = false;
 | |
|     recalculate |= vertexIndices.isLocalModified(); 
 | |
|     recalculate |= mesh->faceVertices.isLocalModified();
 | |
|     recalculate |= mesh->holes.isLocalModified();
 | |
| 
 | |
|     /* check if we can simply update the half edges */
 | |
|     bool update = false;
 | |
|     update |= mesh->topology[0].vertexIndices.isLocalModified(); // we use this buffer to copy creases to interpolation topologies
 | |
|     update |= mesh->edge_creases.isLocalModified();
 | |
|     update |= mesh->edge_crease_weights.isLocalModified();
 | |
|     update |= mesh->vertex_creases.isLocalModified();
 | |
|     update |= mesh->vertex_crease_weights.isLocalModified(); 
 | |
|     update |= mesh->levels.isLocalModified();
 | |
| 
 | |
|     /* now either recalculate or update the half edges */
 | |
|     if (recalculate) calculateHalfEdges();
 | |
|     else if (update) updateHalfEdges();
 | |
|    
 | |
|     /* cleanup some state for static scenes */
 | |
|     /* if (mesh->scene_ == nullptr || mesh->scene_->isStaticAccel()) 
 | |
|     {
 | |
|       halfEdges0.clear();
 | |
|       halfEdges1.clear();
 | |
|     } */
 | |
| 
 | |
|     /* clear modified state of all buffers */
 | |
|     vertexIndices.clearLocalModified(); 
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::printStatistics()
 | |
|   {
 | |
|     size_t numBilinearFaces = 0;
 | |
|     size_t numRegularQuadFaces = 0;
 | |
|     size_t numIrregularQuadFaces = 0;
 | |
|     size_t numComplexFaces = 0;
 | |
|     
 | |
|     for (size_t e=0, f=0; f<numFaces(); e+=faceVertices[f++]) 
 | |
|     {
 | |
|       switch (topology[0].halfEdges[e].patch_type) {
 | |
|       case HalfEdge::BILINEAR_PATCH      : numBilinearFaces++;   break;
 | |
|       case HalfEdge::REGULAR_QUAD_PATCH  : numRegularQuadFaces++;   break;
 | |
|       case HalfEdge::IRREGULAR_QUAD_PATCH: numIrregularQuadFaces++; break;
 | |
|       case HalfEdge::COMPLEX_PATCH       : numComplexFaces++;   break;
 | |
|       }
 | |
|     }
 | |
|     
 | |
|     std::cout << "numFaces = " << numFaces() << ", " 
 | |
|               << "numBilinearFaces = " << numBilinearFaces << " (" << 100.0f * numBilinearFaces / numFaces() << "%), " 
 | |
|               << "numRegularQuadFaces = " << numRegularQuadFaces << " (" << 100.0f * numRegularQuadFaces / numFaces() << "%), " 
 | |
|               << "numIrregularQuadFaces " << numIrregularQuadFaces << " (" << 100.0f * numIrregularQuadFaces / numFaces() << "%) " 
 | |
|               << "numComplexFaces " << numComplexFaces << " (" << 100.0f * numComplexFaces / numFaces() << "%) " 
 | |
|               << std::endl;
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::initializeHalfEdgeStructures ()
 | |
|   {
 | |
|     double t0 = getSeconds();
 | |
| 
 | |
|     invalid_face.resize(numFaces()*numTimeSteps);
 | |
|  
 | |
|     /* calculate start edge of each face */
 | |
|     faceStartEdge.resize(numFaces());
 | |
|     
 | |
|     if (faceVertices.isLocalModified())
 | |
|     {
 | |
|       numHalfEdges = parallel_prefix_sum(faceVertices,faceStartEdge,numFaces(),0,std::plus<unsigned>());
 | |
| 
 | |
|       /* calculate face of each half edge */
 | |
|       halfEdgeFace.resize(numHalfEdges);
 | |
|       for (size_t f=0, h=0; f<numFaces(); f++)
 | |
|         for (size_t e=0; e<faceVertices[f]; e++)
 | |
|           halfEdgeFace[h++] = (unsigned int) f;
 | |
|     }
 | |
|     
 | |
|     /* create set with all vertex creases */
 | |
|     if (vertex_creases.isLocalModified() || vertex_crease_weights.isLocalModified())
 | |
|       vertexCreaseMap->vertexCreaseMap.init(vertex_creases,vertex_crease_weights);
 | |
|     
 | |
|     /* create map with all edge creases */
 | |
|     if (edge_creases.isLocalModified() || edge_crease_weights.isLocalModified())
 | |
|       edgeCreaseMap->edgeCreaseMap.init(edge_creases,edge_crease_weights);
 | |
| 
 | |
|     /* create set with all holes */
 | |
|     if (holes.isLocalModified())
 | |
|       holeSet->holeSet.init(holes);
 | |
| 
 | |
|     /* create topology */
 | |
|     for (auto& t: topology)
 | |
|       t.initializeHalfEdgeStructures();
 | |
| 
 | |
|     /* create interpolation cache mapping for interpolatable meshes */
 | |
|     for (size_t i=0; i<vertex_buffer_tags.size(); i++)
 | |
|       vertex_buffer_tags[i].resize(numFaces()*numInterpolationSlots4(vertices[i].getStride()));
 | |
|     for (size_t i=0; i<vertexAttribs.size(); i++)
 | |
|       if (vertexAttribs[i]) vertex_attrib_buffer_tags[i].resize(numFaces()*numInterpolationSlots4(vertexAttribs[i].getStride()));
 | |
| 
 | |
|     /* cleanup some state for static scenes */
 | |
|     /* if (scene_ == nullptr || scene_->isStaticAccel()) 
 | |
|     {
 | |
|       vertexCreaseMap->vertexCreaseMap.clear();
 | |
|       edgeCreaseMap->edgeCreaseMap.clear();
 | |
|     } */
 | |
| 
 | |
|     /* clear modified state of all buffers */
 | |
|     faceVertices.clearLocalModified();
 | |
|     holes.clearLocalModified();
 | |
|     for (auto& buffer : vertices) buffer.clearLocalModified(); 
 | |
|     levels.clearLocalModified();
 | |
|     edge_creases.clearLocalModified();
 | |
|     edge_crease_weights.clearLocalModified();
 | |
|     vertex_creases.clearLocalModified();
 | |
|     vertex_crease_weights.clearLocalModified();
 | |
| 
 | |
|     double t1 = getSeconds();
 | |
| 
 | |
|     /* print statistics in verbose mode */
 | |
|     if (device->verbosity(2)) {
 | |
|       std::cout << "half edge generation = " << 1000.0*(t1-t0) << "ms, " << 1E-6*double(numHalfEdges)/(t1-t0) << "M/s" << std::endl;
 | |
|       printStatistics();
 | |
|     }
 | |
|   }
 | |
| 
 | |
|   bool SubdivMesh::verify () 
 | |
|   {
 | |
|     /*! verify consistent size of vertex arrays */
 | |
|     if (vertices.size() == 0) return false;
 | |
|     for (const auto& buffer : vertices)
 | |
|       if (buffer.size() != numVertices())
 | |
|         return false;
 | |
| 
 | |
|     /*! verify vertex indices */
 | |
|     if (!topology[0].verify(numVertices()))
 | |
|       return false;
 | |
| 
 | |
|     for (auto& b : vertexAttribs)
 | |
|       if (!topology[b.userData].verify(b.size()))
 | |
|         return false;
 | |
| 
 | |
|     /*! verify vertices */
 | |
|     for (const auto& buffer : vertices)
 | |
|       for (size_t i=0; i<buffer.size(); i++)
 | |
| 	if (!isvalid(buffer[i])) 
 | |
| 	  return false;
 | |
| 
 | |
|     return true;
 | |
|   }
 | |
| 
 | |
|   void SubdivMesh::commit () 
 | |
|   {
 | |
|     initializeHalfEdgeStructures();
 | |
|     Geometry::commit();
 | |
|   }
 | |
| 
 | |
|   unsigned int SubdivMesh::getFirstHalfEdge(unsigned int faceID)
 | |
|   {
 | |
|     if (faceID >= numFaces())
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid face");
 | |
| 
 | |
|     return faceStartEdge[faceID];
 | |
|   }
 | |
| 
 | |
|   unsigned int SubdivMesh::getFace(unsigned int edgeID)
 | |
|   {
 | |
|     if (edgeID >= numHalfEdges)
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid edge");
 | |
| 
 | |
|     return halfEdgeFace[edgeID];
 | |
|   }
 | |
|     
 | |
|   unsigned int SubdivMesh::getNextHalfEdge(unsigned int edgeID)
 | |
|   {
 | |
|     if (edgeID >= numHalfEdges)
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid half edge");
 | |
| 
 | |
|     return edgeID + topology[0].halfEdges[edgeID].next_half_edge_ofs;
 | |
|   }
 | |
| 
 | |
|   unsigned int SubdivMesh::getPreviousHalfEdge(unsigned int edgeID)
 | |
|   {
 | |
|      if (edgeID >= numHalfEdges)
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid half edge");
 | |
| 
 | |
|     return edgeID + topology[0].halfEdges[edgeID].prev_half_edge_ofs;
 | |
|   }
 | |
| 
 | |
|   unsigned int SubdivMesh::getOppositeHalfEdge(unsigned int topologyID, unsigned int edgeID)
 | |
|   {
 | |
|     if (topologyID >= topology.size())
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid topology");
 | |
|     
 | |
|     if (edgeID >= numHalfEdges)
 | |
|       throw_RTCError(RTC_ERROR_INVALID_ARGUMENT, "invalid half edge");
 | |
| 
 | |
|     return edgeID + topology[topologyID].halfEdges[edgeID].opposite_half_edge_ofs;
 | |
|   }
 | |
|   
 | |
| #endif
 | |
| 
 | |
|   namespace isa
 | |
|   {
 | |
|     SubdivMesh* createSubdivMesh(Device* device) {
 | |
|       return new SubdivMeshISA(device);
 | |
|     }
 | |
|     
 | |
|     void SubdivMeshISA::interpolate(const RTCInterpolateArguments* const args)
 | |
|     {
 | |
|       unsigned int primID = args->primID;
 | |
|       float u = args->u;
 | |
|       float v = args->v;
 | |
|       RTCBufferType bufferType = args->bufferType;
 | |
|       unsigned int bufferSlot = args->bufferSlot;
 | |
|       float* P = args->P;
 | |
|       float* dPdu = args->dPdu;
 | |
|       float* dPdv = args->dPdv;
 | |
|       float* ddPdudu = args->ddPdudu;
 | |
|       float* ddPdvdv = args->ddPdvdv;
 | |
|       float* ddPdudv = args->ddPdudv;
 | |
|       unsigned int valueCount = args->valueCount;
 | |
|       
 | |
|       /* calculate base pointer and stride */
 | |
|       assert((bufferType == RTC_BUFFER_TYPE_VERTEX && bufferSlot < RTC_MAX_TIME_STEP_COUNT) ||
 | |
|              (bufferType == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE && bufferSlot < RTC_MAX_USER_VERTEX_BUFFERS));
 | |
|       const char* src = nullptr; 
 | |
|       size_t stride = 0;
 | |
|       std::vector<SharedLazyTessellationCache::CacheEntry>* baseEntry = nullptr;
 | |
|       Topology* topo = nullptr;
 | |
|       if (bufferType == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE) {
 | |
|         assert(bufferSlot < vertexAttribs.size());
 | |
|         src    = vertexAttribs[bufferSlot].getPtr();
 | |
|         stride = vertexAttribs[bufferSlot].getStride();
 | |
|         baseEntry = &vertex_attrib_buffer_tags[bufferSlot];
 | |
|         int topologyID = vertexAttribs[bufferSlot].userData;
 | |
|         topo = &topology[topologyID];
 | |
|       } else {
 | |
|         assert(bufferSlot < numTimeSteps);
 | |
|         src    = vertices[bufferSlot].getPtr();
 | |
|         stride = vertices[bufferSlot].getStride();
 | |
|         baseEntry = &vertex_buffer_tags[bufferSlot];
 | |
|         topo = &topology[0];
 | |
|       }
 | |
|       
 | |
|       bool has_P = P;
 | |
|       bool has_dP = dPdu;     assert(!has_dP  || dPdv);
 | |
|       bool has_ddP = ddPdudu; assert(!has_ddP || (ddPdvdv && ddPdudu));
 | |
|       
 | |
|       for (unsigned int i=0; i<valueCount; i+=4)
 | |
|       {
 | |
|         vfloat4 Pt, dPdut, dPdvt, ddPdudut, ddPdvdvt, ddPdudvt;
 | |
|         isa::PatchEval<vfloat4,vfloat4>(baseEntry->at(interpolationSlot(primID,i/4,stride)),commitCounter,
 | |
|                                         topo->getHalfEdge(primID),src+i*sizeof(float),stride,u,v,
 | |
|                                         has_P ? &Pt : nullptr, 
 | |
|                                         has_dP ? &dPdut : nullptr, 
 | |
|                                         has_dP ? &dPdvt : nullptr,
 | |
|                                         has_ddP ? &ddPdudut : nullptr, 
 | |
|                                         has_ddP ? &ddPdvdvt : nullptr, 
 | |
|                                         has_ddP ? &ddPdudvt : nullptr);
 | |
|         
 | |
|         if (has_P) {
 | |
|           for (size_t j=i; j<min(i+4,valueCount); j++) 
 | |
|             P[j] = Pt[j-i];
 | |
|         }
 | |
|         if (has_dP) 
 | |
|         {
 | |
|           for (size_t j=i; j<min(i+4,valueCount); j++) {
 | |
|             dPdu[j] = dPdut[j-i];
 | |
|             dPdv[j] = dPdvt[j-i];
 | |
|           }
 | |
|         }
 | |
|         if (has_ddP) 
 | |
|         {
 | |
|           for (size_t j=i; j<min(i+4,valueCount); j++) {
 | |
|             ddPdudu[j] = ddPdudut[j-i];
 | |
|             ddPdvdv[j] = ddPdvdvt[j-i];
 | |
|             ddPdudv[j] = ddPdudvt[j-i];
 | |
|           }
 | |
|         }
 | |
|       }
 | |
|     }
 | |
|     
 | |
|     void SubdivMeshISA::interpolateN(const RTCInterpolateNArguments* const args)
 | |
|     {
 | |
|       const void* valid_i = args->valid;
 | |
|       const unsigned* primIDs = args->primIDs;
 | |
|       const float* u = args->u;
 | |
|       const float* v = args->v;
 | |
|       unsigned int N = args->N;
 | |
|       RTCBufferType bufferType = args->bufferType;
 | |
|       unsigned int bufferSlot = args->bufferSlot;
 | |
|       float* P = args->P;
 | |
|       float* dPdu = args->dPdu;
 | |
|       float* dPdv = args->dPdv;
 | |
|       float* ddPdudu = args->ddPdudu;
 | |
|       float* ddPdvdv = args->ddPdvdv;
 | |
|       float* ddPdudv = args->ddPdudv;
 | |
|       unsigned int valueCount = args->valueCount;
 | |
|     
 | |
|       /* calculate base pointer and stride */
 | |
|       assert((bufferType == RTC_BUFFER_TYPE_VERTEX && bufferSlot < RTC_MAX_TIME_STEP_COUNT) ||
 | |
|              (bufferType == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE && bufferSlot < RTC_MAX_USER_VERTEX_BUFFERS));
 | |
|       const char* src = nullptr; 
 | |
|       size_t stride = 0;
 | |
|       std::vector<SharedLazyTessellationCache::CacheEntry>* baseEntry = nullptr;
 | |
|       Topology* topo = nullptr;
 | |
|       if (bufferType == RTC_BUFFER_TYPE_VERTEX_ATTRIBUTE) {
 | |
|         assert(bufferSlot < vertexAttribs.size());
 | |
|         src    = vertexAttribs[bufferSlot].getPtr();
 | |
|         stride = vertexAttribs[bufferSlot].getStride();
 | |
|         baseEntry = &vertex_attrib_buffer_tags[bufferSlot];
 | |
|         int topologyID = vertexAttribs[bufferSlot].userData;
 | |
|         topo = &topology[topologyID];
 | |
|       } else {
 | |
|         assert(bufferSlot < numTimeSteps);
 | |
|         src    = vertices[bufferSlot].getPtr();
 | |
|         stride = vertices[bufferSlot].getStride();
 | |
|         baseEntry = &vertex_buffer_tags[bufferSlot];
 | |
|         topo = &topology[0];
 | |
|       }
 | |
|       
 | |
|       const int* valid = (const int*) valid_i;
 | |
|       
 | |
|       for (size_t i=0; i<N; i+=4) 
 | |
|       {
 | |
|         vbool4 valid1 = vint4(int(i))+vint4(step) < vint4(int(N));
 | |
|         if (valid) valid1 &= vint4::loadu(&valid[i]) == vint4(-1);
 | |
|         if (none(valid1)) continue;
 | |
|         
 | |
|         const vuint4 primID = vuint4::loadu(&primIDs[i]);
 | |
|         const vfloat4 uu = vfloat4::loadu(&u[i]);
 | |
|         const vfloat4 vv = vfloat4::loadu(&v[i]);
 | |
|         
 | |
|         foreach_unique(valid1,primID,[&](const vbool4& valid1, const unsigned int primID)
 | |
|                        {
 | |
|                          for (unsigned int j=0; j<valueCount; j+=4) 
 | |
|                          {
 | |
|                            const size_t M = min(4u,valueCount-j);
 | |
|                            isa::PatchEvalSimd<vbool4,vint4,vfloat4,vfloat4>(baseEntry->at(interpolationSlot(primID,j/4,stride)),commitCounter,
 | |
|                                                                             topo->getHalfEdge(primID),src+j*sizeof(float),stride,valid1,uu,vv,
 | |
|                                                                             P ? P+j*N+i : nullptr,
 | |
|                                                                             dPdu ? dPdu+j*N+i : nullptr,
 | |
|                                                                             dPdv ? dPdv+j*N+i : nullptr,
 | |
|                                                                             ddPdudu ? ddPdudu+j*N+i : nullptr,
 | |
|                                                                             ddPdvdv ? ddPdvdv+j*N+i : nullptr,
 | |
|                                                                             ddPdudv ? ddPdudv+j*N+i : nullptr,
 | |
|                                                                             N,M);
 | |
|                          }
 | |
|                        });
 | |
|       }
 | |
|     }
 | |
|   }
 | |
| }
 |