327 lines
14 KiB
C++
327 lines
14 KiB
C++
/*
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---------------------------------------------------------------------------
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Open Asset Import Library (assimp)
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---------------------------------------------------------------------------
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Copyright (c) 2006-2021, assimp team
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All rights reserved.
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Redistribution and use of this software in source and binary forms,
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with or without modification, are permitted provided that the following
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conditions are met:
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* Redistributions of source code must retain the above
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copyright notice, this list of conditions and the
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following disclaimer.
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* Redistributions in binary form must reproduce the above
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copyright notice, this list of conditions and the
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following disclaimer in the documentation and/or other
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materials provided with the distribution.
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* Neither the name of the assimp team, nor the names of its
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contributors may be used to endorse or promote products
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derived from this software without specific prior
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written permission of the assimp team.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
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OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
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SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
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LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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---------------------------------------------------------------------------
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*/
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/** @file Implementation of the helper class to quickly find vertices close to a given position */
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#include <assimp/SpatialSort.h>
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#include <assimp/ai_assert.h>
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using namespace Assimp;
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// CHAR_BIT seems to be defined under MVSC, but not under GCC. Pray that the correct value is 8.
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#ifndef CHAR_BIT
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#define CHAR_BIT 8
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#endif
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const aiVector3D PlaneInit(0.8523f, 0.34321f, 0.5736f);
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// ------------------------------------------------------------------------------------------------
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// Constructs a spatially sorted representation from the given position array.
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// define the reference plane. We choose some arbitrary vector away from all basic axises
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// in the hope that no model spreads all its vertices along this plane.
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SpatialSort::SpatialSort(const aiVector3D *pPositions, unsigned int pNumPositions, unsigned int pElementOffset) :
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mPlaneNormal(PlaneInit) {
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mPlaneNormal.Normalize();
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Fill(pPositions, pNumPositions, pElementOffset);
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}
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// ------------------------------------------------------------------------------------------------
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SpatialSort::SpatialSort() :
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mPlaneNormal(PlaneInit) {
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mPlaneNormal.Normalize();
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}
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// ------------------------------------------------------------------------------------------------
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// Destructor
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SpatialSort::~SpatialSort() {
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// empty
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}
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// ------------------------------------------------------------------------------------------------
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void SpatialSort::Fill(const aiVector3D *pPositions, unsigned int pNumPositions,
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unsigned int pElementOffset,
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bool pFinalize /*= true */) {
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mPositions.clear();
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Append(pPositions, pNumPositions, pElementOffset, pFinalize);
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}
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// ------------------------------------------------------------------------------------------------
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void SpatialSort::Finalize() {
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std::sort(mPositions.begin(), mPositions.end());
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}
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// ------------------------------------------------------------------------------------------------
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void SpatialSort::Append(const aiVector3D *pPositions, unsigned int pNumPositions,
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unsigned int pElementOffset,
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bool pFinalize /*= true */) {
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// store references to all given positions along with their distance to the reference plane
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const size_t initial = mPositions.size();
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mPositions.reserve(initial + (pFinalize ? pNumPositions : pNumPositions * 2));
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for (unsigned int a = 0; a < pNumPositions; a++) {
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const char *tempPointer = reinterpret_cast<const char *>(pPositions);
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const aiVector3D *vec = reinterpret_cast<const aiVector3D *>(tempPointer + a * pElementOffset);
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// store position by index and distance
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ai_real distance = *vec * mPlaneNormal;
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mPositions.push_back(Entry(static_cast<unsigned int>(a + initial), *vec, distance));
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}
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if (pFinalize) {
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// now sort the array ascending by distance.
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Finalize();
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}
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}
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// ------------------------------------------------------------------------------------------------
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// Returns an iterator for all positions close to the given position.
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void SpatialSort::FindPositions(const aiVector3D &pPosition,
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ai_real pRadius, std::vector<unsigned int> &poResults) const {
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const ai_real dist = pPosition * mPlaneNormal;
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const ai_real minDist = dist - pRadius, maxDist = dist + pRadius;
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// clear the array
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poResults.clear();
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// quick check for positions outside the range
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if (mPositions.size() == 0)
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return;
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if (maxDist < mPositions.front().mDistance)
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return;
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if (minDist > mPositions.back().mDistance)
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return;
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// do a binary search for the minimal distance to start the iteration there
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unsigned int index = (unsigned int)mPositions.size() / 2;
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unsigned int binaryStepSize = (unsigned int)mPositions.size() / 4;
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while (binaryStepSize > 1) {
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if (mPositions[index].mDistance < minDist)
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index += binaryStepSize;
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else
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index -= binaryStepSize;
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binaryStepSize /= 2;
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}
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// depending on the direction of the last step we need to single step a bit back or forth
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// to find the actual beginning element of the range
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while (index > 0 && mPositions[index].mDistance > minDist)
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index--;
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while (index < (mPositions.size() - 1) && mPositions[index].mDistance < minDist)
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index++;
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// Mow start iterating from there until the first position lays outside of the distance range.
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// Add all positions inside the distance range within the given radius to the result aray
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std::vector<Entry>::const_iterator it = mPositions.begin() + index;
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const ai_real pSquared = pRadius * pRadius;
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while (it->mDistance < maxDist) {
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if ((it->mPosition - pPosition).SquareLength() < pSquared)
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poResults.push_back(it->mIndex);
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++it;
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if (it == mPositions.end())
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break;
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}
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// that's it
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}
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namespace {
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// Binary, signed-integer representation of a single-precision floating-point value.
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// IEEE 754 says: "If two floating-point numbers in the same format are ordered then they are
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// ordered the same way when their bits are reinterpreted as sign-magnitude integers."
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// This allows us to convert all floating-point numbers to signed integers of arbitrary size
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// and then use them to work with ULPs (Units in the Last Place, for high-precision
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// computations) or to compare them (integer comparisons are faster than floating-point
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// comparisons on many platforms).
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typedef ai_int BinFloat;
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// --------------------------------------------------------------------------------------------
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// Converts the bit pattern of a floating-point number to its signed integer representation.
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BinFloat ToBinary(const ai_real &pValue) {
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// If this assertion fails, signed int is not big enough to store a float on your platform.
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// Please correct the declaration of BinFloat a few lines above - but do it in a portable,
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// #ifdef'd manner!
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static_assert(sizeof(BinFloat) >= sizeof(ai_real), "sizeof(BinFloat) >= sizeof(ai_real)");
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#if defined(_MSC_VER)
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// If this assertion fails, Visual C++ has finally moved to ILP64. This means that this
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// code has just become legacy code! Find out the current value of _MSC_VER and modify
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// the #if above so it evaluates false on the current and all upcoming VC versions (or
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// on the current platform, if LP64 or LLP64 are still used on other platforms).
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static_assert(sizeof(BinFloat) == sizeof(ai_real), "sizeof(BinFloat) == sizeof(ai_real)");
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// This works best on Visual C++, but other compilers have their problems with it.
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const BinFloat binValue = reinterpret_cast<BinFloat const &>(pValue);
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//::memcpy(&binValue, &pValue, sizeof(pValue));
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//return binValue;
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#else
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// On many compilers, reinterpreting a float address as an integer causes aliasing
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// problems. This is an ugly but more or less safe way of doing it.
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union {
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ai_real asFloat;
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BinFloat asBin;
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} conversion;
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conversion.asBin = 0; // zero empty space in case sizeof(BinFloat) > sizeof(float)
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conversion.asFloat = pValue;
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const BinFloat binValue = conversion.asBin;
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#endif
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// floating-point numbers are of sign-magnitude format, so find out what signed number
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// representation we must convert negative values to.
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// See http://en.wikipedia.org/wiki/Signed_number_representations.
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const BinFloat mask = BinFloat(1) << (CHAR_BIT * sizeof(BinFloat) - 1);
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// Two's complement?
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const bool DefaultValue = ((-42 == (~42 + 1)) && (binValue & mask));
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const bool OneComplement = ((-42 == ~42) && (binValue & mask));
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if (DefaultValue)
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return mask - binValue;
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// One's complement?
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else if (OneComplement)
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return BinFloat(-0) - binValue;
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// Sign-magnitude? -0 = 1000... binary
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return binValue;
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}
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} // namespace
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// ------------------------------------------------------------------------------------------------
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// Fills an array with indices of all positions identical to the given position. In opposite to
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// FindPositions(), not an epsilon is used but a (very low) tolerance of four floating-point units.
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void SpatialSort::FindIdenticalPositions(const aiVector3D &pPosition, std::vector<unsigned int> &poResults) const {
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// Epsilons have a huge disadvantage: they are of constant precision, while floating-point
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// values are of log2 precision. If you apply e=0.01 to 100, the epsilon is rather small, but
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// if you apply it to 0.001, it is enormous.
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// The best way to overcome this is the unit in the last place (ULP). A precision of 2 ULPs
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// tells us that a float does not differ more than 2 bits from the "real" value. ULPs are of
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// logarithmic precision - around 1, they are 1*(2^24) and around 10000, they are 0.00125.
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// For standard C math, we can assume a precision of 0.5 ULPs according to IEEE 754. The
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// incoming vertex positions might have already been transformed, probably using rather
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// inaccurate SSE instructions, so we assume a tolerance of 4 ULPs to safely identify
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// identical vertex positions.
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static const int toleranceInULPs = 4;
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// An interesting point is that the inaccuracy grows linear with the number of operations:
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// multiplying to numbers, each inaccurate to four ULPs, results in an inaccuracy of four ULPs
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// plus 0.5 ULPs for the multiplication.
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// To compute the distance to the plane, a dot product is needed - that is a multiplication and
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// an addition on each number.
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static const int distanceToleranceInULPs = toleranceInULPs + 1;
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// The squared distance between two 3D vectors is computed the same way, but with an additional
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// subtraction.
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static const int distance3DToleranceInULPs = distanceToleranceInULPs + 1;
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// Convert the plane distance to its signed integer representation so the ULPs tolerance can be
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// applied. For some reason, VC won't optimize two calls of the bit pattern conversion.
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const BinFloat minDistBinary = ToBinary(pPosition * mPlaneNormal) - distanceToleranceInULPs;
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const BinFloat maxDistBinary = minDistBinary + 2 * distanceToleranceInULPs;
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// clear the array in this strange fashion because a simple clear() would also deallocate
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// the array which we want to avoid
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poResults.resize(0);
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// do a binary search for the minimal distance to start the iteration there
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unsigned int index = (unsigned int)mPositions.size() / 2;
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unsigned int binaryStepSize = (unsigned int)mPositions.size() / 4;
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while (binaryStepSize > 1) {
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// Ugly, but conditional jumps are faster with integers than with floats
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if (minDistBinary > ToBinary(mPositions[index].mDistance))
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index += binaryStepSize;
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else
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index -= binaryStepSize;
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binaryStepSize /= 2;
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}
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// depending on the direction of the last step we need to single step a bit back or forth
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// to find the actual beginning element of the range
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while (index > 0 && minDistBinary < ToBinary(mPositions[index].mDistance))
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index--;
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while (index < (mPositions.size() - 1) && minDistBinary > ToBinary(mPositions[index].mDistance))
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index++;
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// Now start iterating from there until the first position lays outside of the distance range.
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// Add all positions inside the distance range within the tolerance to the result array
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std::vector<Entry>::const_iterator it = mPositions.begin() + index;
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while (ToBinary(it->mDistance) < maxDistBinary) {
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if (distance3DToleranceInULPs >= ToBinary((it->mPosition - pPosition).SquareLength()))
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poResults.push_back(it->mIndex);
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++it;
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if (it == mPositions.end())
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break;
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}
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// that's it
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}
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// ------------------------------------------------------------------------------------------------
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unsigned int SpatialSort::GenerateMappingTable(std::vector<unsigned int> &fill, ai_real pRadius) const {
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fill.resize(mPositions.size(), UINT_MAX);
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ai_real dist, maxDist;
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unsigned int t = 0;
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const ai_real pSquared = pRadius * pRadius;
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for (size_t i = 0; i < mPositions.size();) {
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dist = mPositions[i].mPosition * mPlaneNormal;
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maxDist = dist + pRadius;
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fill[mPositions[i].mIndex] = t;
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const aiVector3D &oldpos = mPositions[i].mPosition;
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for (++i; i < fill.size() && mPositions[i].mDistance < maxDist && (mPositions[i].mPosition - oldpos).SquareLength() < pSquared; ++i) {
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fill[mPositions[i].mIndex] = t;
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}
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++t;
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}
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#ifdef ASSIMP_BUILD_DEBUG
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// debug invariant: mPositions[i].mIndex values must range from 0 to mPositions.size()-1
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for (size_t i = 0; i < fill.size(); ++i) {
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ai_assert(fill[i] < mPositions.size());
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}
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#endif
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return t;
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}
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