4b665fa82b
URDF import demo: add COLLADA .dae file support add FiniteElementMethod demo, extracted from the OpenTissue library (under the zlib license) don't crash if loading an invalid STL file add comparison with Assimp for COLLADA file loading (disabled by default, to avoid library dependency) Gwen: disable some flags that make the build incompatible
94 lines
3.4 KiB
C++
94 lines
3.4 KiB
C++
#ifndef OPENTISSUE_DYNAMICS_FEM_FEM_COMPUTE_VOLUME_H
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#define OPENTISSUE_DYNAMICS_FEM_FEM_COMPUTE_VOLUME_H
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//
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// OpenTissue Template Library
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// - A generic toolbox for physics-based modeling and simulation.
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// Copyright (C) 2008 Department of Computer Science, University of Copenhagen.
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//
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// OTTL is licensed under zlib: http://opensource.org/licenses/zlib-license.php
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//
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#include <OpenTissue/configuration.h>
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namespace OpenTissue
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{
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namespace fem
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{
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namespace detail
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{
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/**
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* Compute volume of tetrahedron.
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*
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* @param e10 edge vector from p0 to p1, i.e. e10 = p1-p0.
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* @param e20 edge vector from p0 to p2, i.e. e20 = p2-p0.
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* @param e30 edge vector from p0 to p3, i.e. e30 = p3-p0.
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*
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* @return The signed volume of the tetrahedra with nodes p0,p1,p2 and p3.
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*/
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template<typename vector3_type>
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inline typename vector3_type::value_type compute_volume(vector3_type const& e10, vector3_type const& e20, vector3_type const& e30)
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{
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typedef typename vector3_type::value_type real_type;
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// Calculate the volume given by:
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// | 1 1 1 1 |
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// | e1x e2x e3x | | p0x p1x p2x p3x |
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// 6V = | e1 \cdot (e2 x e3) | = | e1y e2y e3y | = 6V | p0y p1y p2y p3y |
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// | e1z e2z e3z | | p0z p1z p2z p3z |
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//
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real_type sixV = e10*(e20 % e30);
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return sixV / 6.0;
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}
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/**
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* Compute Tetrahedron Volume
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*
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* @param p0
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* @param p1
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* @param p2
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* @param p3
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*
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* @return The signed volume of the tetrahedra with nodes p0,p1,p2 and p3.
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*/
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template<typename vector3_type>
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inline typename vector3_type::value_type compute_volume(vector3_type const & p0,vector3_type const & p1,vector3_type const & p2,vector3_type const & p3)
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{
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typedef typename vector3_type::value_type real_type;
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real_type d = p0(0);
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real_type d4 = p0(1);
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real_type d8 = p0(2);
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real_type d1 = p1(0) - d;
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real_type d5 = p1(1) - d4;
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real_type d9 = p1(2) - d8;
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real_type d2 = p2(0) - d;
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real_type d6 = p2(1) - d4;
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real_type d10 = p2(2) - d8;
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real_type d3 = p3(0) - d;
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real_type d7 = p3(1) - d4;
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real_type d11 = p3(2) - d8;
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real_type d12 = (d1 * d6 * d11 + d2 * d7 * d9 + d3 * d5 * d10) - d1 * d7 * d10 - d2 * d5 * d11 - d3 * d6 * d9;
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return d12 / 6.0;
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/*
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** From Zienkiewicz & Taylor p.637
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** V = 1/6*det( 1 x0 y0 z0; 1 x1 y1 z1; 1 x2 y2 z2; 1 x3 y3 z3)
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** where x0 = n0->i; y0 = n0(1); ...
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** Calculated by Mathematica ;-)
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*/
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/*
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return (p0(2)*p1(1)*p2(0) - p0(1)*p1(2)*p2(0) - p0(2)*p1(0)*p2(1)
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+ p0(0)*p1(2)*p2(1) + p0(1)*p1(0)*p2(2) - p0(0)*p1(1)*p2(2)
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- p0(2)*p1(1)*p3(0) + p0(1)*p1(2)*p3(0) + p0(2)*p2(1)*p3(0)
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- p1(2)*p2(1)*p3(0) - p0(1)*p2(2)*p3(0) + p1(1)*p2(2)*p3(0)
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+ p0(2)*p1(0)*p3(1) - p0(0)*p1(2)*p3(1) - p0(2)*p2(0)*p3(1)
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+ p1(2)*p2(0)*p3(1) + p0(0)*p2(2)*p3(1) - p1(0)*p2(2)*p3(1)
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- p0(1)*p1(0)*p3(2) + p0(0)*p1(1)*p3(2) + p0(1)*p2(0)*p3(2)
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- p1(1)*p2(0)*p3(2) - p0(0)*p2(1)*p3(2) + p1(0)*p2(1)*p3(2))/6.;
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*/
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}
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} // namespace detail
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} // namespace fem
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} // namespace OpenTissue
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//OPENTISSUE_DYNAMICS_FEM_FEM_COMPUTE_VOLUME_H
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#endif
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