NvCloth 1.1.0 Release. (22041545)

author: Marijn Tamis <[email protected]> 2017-04-28 14:19:07 +0200
committer: Marijn Tamis <[email protected]> 2017-04-28 14:19:07 +0200
commit: b350eb5f4d44e8448115796144375d79438d74ae (patch)
tree: 8e102e8c28f45a1b87bd335ceee4f33c3d4ee7c2 /NvCloth/docs/documentation/Solver
parent: Add visual samples. (diff)
download: nvcloth-b350eb5f4d44e8448115796144375d79438d74ae.tar.xz
nvcloth-b350eb5f4d44e8448115796144375d79438d74ae.zip
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-    <div class="related">
-      <h3>Navigation</h3>
-      <ul>
-        <li><a href="../NvCloth.html">NVIDIA NvCloth Documentation</a> &raquo;</li> 
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-      <div class="documentwrapper">
-        <div class="bodywrapper">
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-            
-  <div class="section" id="internal-solver-function-algorithm-documentation">
-<h1>Internal solver function/algorithm documentation<a class="headerlink" href="#internal-solver-function-algorithm-documentation" title="Permalink to this headline">¶</a></h1>
-<p>This document describes the internal workings of the solver.
-We describe how the different parts work independent from platform specific features. Although we might occasionally comment on particular implementation details.</p>
-<p>Todo: give this solver a name, so that we can differentiate when a new/different solver is added.</p>
-<div class="toggle container">
-<div class="header container">
-Show/Hide Code</div>
-<div class="togglecontent container">
-test togglecontent</div>
-</div>
-<div class="section" id="overview">
-<h2>Overview<a class="headerlink" href="#overview" title="Permalink to this headline">¶</a></h2>
-<p>Overview of the general algorithm goes here.</p>
-<ul class="simple">
-<li>Integrate particles (integrateParticles())</li>
-<li>Simulate wind/drag/lift (applyWind())</li>
-<li>Distance constraints (constrainMotion())</li>
-<li>Tether constraints (constrainTether())</li>
-<li>Solve edge constraints (solveFabric())</li>
-<li>Solve separation constraints (constrainSeparation())</li>
-<li>Collision (collideParticles())</li>
-<li>Self collision (selfCollideParticles())</li>
-<li>Update sleep state (updateSleepState())</li>
-</ul>
-</div>
-<div class="section" id="particle-invmass-w-component">
-<h2>Particle invMass w component<a class="headerlink" href="#particle-invmass-w-component" title="Permalink to this headline">¶</a></h2>
-<p>Todo: check and rewrite:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="c1">// note on invMass (stored in current/previous positions.w):</span>
-<span class="c1">// integrateParticles()</span>
-<span class="c1">//   - if(current.w == 0) current.w = previous.w</span>
-<span class="c1">// constraintMotion()</span>
-<span class="c1">//   - if(constraint.radius &lt;= 0) current.w = 0</span>
-<span class="c1">// computeBounds()</span>
-<span class="c1">//   - if(current.w &gt; 0) current.w = previous.w</span>
-<span class="c1">// collideParticles()</span>
-<span class="c1">//   - if(collides) current.w *= 1/massScale</span>
-<span class="c1">// after simulate()</span>
-<span class="c1">//   - previous.w: original invMass as set by user</span>
-<span class="c1">//   - current.w: zeroed by motion constraints and mass-scaled by collision</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="slack">
-<h2>Slack<a class="headerlink" href="#slack" title="Permalink to this headline">¶</a></h2>
-<p>The position constraint for keeping distance between points a and b is usually written as:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">error</span>  <span class="o">=</span> <span class="o">|</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="o">|</span> <span class="o">-</span> <span class="n">restLength</span>
-<span class="n">offset</span> <span class="o">=</span> <span class="n">error</span> <span class="o">*</span> <span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span><span class="o">/|</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="o">|</span>
-       <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span> <span class="o">-</span> <span class="n">restLength</span><span class="o">*</span><span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span><span class="o">/|</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="o">|</span>
-</pre></div>
-</div>
-<p>The equation calculating <em>slack</em> pops up often in the solver code.
-This does exactly the same as the above:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">slack</span>  <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">restLength</span> <span class="o">/</span> <span class="o">|</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="o">|</span>
-<span class="n">offset</span> <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span> <span class="o">*</span> <span class="n">slack</span>
-       <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span> <span class="o">-</span> <span class="n">restLength</span><span class="o">*</span><span class="p">(</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="p">)</span><span class="o">/|</span><span class="n">b</span><span class="o">-</span><span class="n">a</span><span class="o">|</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="integration">
-<h2>Integration<a class="headerlink" href="#integration" title="Permalink to this headline">¶</a></h2>
-<p>The first step of the cloth simulation is the integration.
-Explicit Euler integration is used to calculate the new position of the particles.
-The velocity of the particles is not stored, instead we use the position from the previous frame to calculate the velocity.
-We need to compensate for differences in delta time. Large fluctuations can cause problems, so the delta time is damped.</p>
-<p>The following pseudo code describes how this is implemented:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="c1">//calculate damping constants from user setting &#39;damping&#39;</span>
-<span class="n">logDamping</span> <span class="o">=</span> <span class="n">log_2</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">damping</span><span class="p">)</span> <span class="c1">//from ClothImpl&lt;T&gt;::setDamping</span>
-<span class="n">dampExponent</span> <span class="o">=</span> <span class="n">stiffnessFrequency</span> <span class="o">*</span> <span class="n">dt1</span> <span class="c1">//from IterationState::create</span>
-
-<span class="c1">//calculate delta time ajustment</span>
-<span class="n">scale</span> <span class="o">=</span> <span class="n">e</span><span class="o">^</span><span class="p">{</span><span class="n">logDamping</span> <span class="o">*</span> <span class="n">dampExponent</span><span class="p">}</span> <span class="o">*</span> <span class="p">{</span><span class="n">dt1</span><span class="o">/</span><span class="n">dt0</span><span class="p">}</span> <span class="c1">//from IterationState::create</span>
-<span class="c1">//Do the integration</span>
-<span class="n">delta</span> <span class="o">=</span> <span class="p">(</span><span class="n">particle_position1</span><span class="o">-</span><span class="n">particle_position0</span><span class="p">)</span> <span class="o">*</span> <span class="n">scale</span> <span class="o">+</span> <span class="n">acceleration</span>
-<span class="n">particle_position1</span> <span class="o">=</span> <span class="n">particle_position1</span> <span class="o">+</span> <span class="n">delta</span>
-</pre></div>
-</div>
-<p>The integration code also replaces the current inverse mass with the previous inverse mass if the current is zero.</p>
-<p>Todo: rotating reference frame.</p>
-<p>Todo: how does damping work?</p>
-</div>
-<div class="section" id="wind-simulation">
-<h2>Wind simulation<a class="headerlink" href="#wind-simulation" title="Permalink to this headline">¶</a></h2>
-<p>Drag and lift simulation is done in the applyWind() function.
-The following algorithm is used:</p>
-<div class="highlight-c++"><pre>for each triangle
-       \(p_j\) is the previous and \(c_j\) is the current position and \(m^{-1}_j\) is the inverse mass of the \(j\)th particle in of the triangle.
-
-       //Calculate current and previous center of the triangle
-       \(c_t = \frac{1}{3} \cdot \left( c_0 + c_1 + c_2 \right)\)
-       \(p_t = \frac{1}{3} \cdot \left( p_0 + p_1 + p_2 \right)\)
-
-       //Position difference including wind (same as flow speed times dt)
-       \(d = c_t - p_t + wind\)
-
-       if rotating reference frame
-               \(d = c_t + R\left(d-c_t\right)\) //where \(R\) is the inverse local space rotation for one solver iteration
-               //Todo check/explain this
-
-       //Unnormalized normal of the triangle
-       \(n = \left(c_2 - c_0\right) \times \left(c_1 - c_0\right) \)
-
-       //Double the area of the triangle
-       \(a = \left|n\right| \)
-
-       \(\Lrg{ \cos\left(\theta\right) = \frac{n \cdot d}{\left|n\right| \cdot \left|d \right|} }\)
-       \(\Lrg{ \sin\left(\theta\right) =  \sqrt{\max(0, 1 - \cos\left(\theta\right)^2)}}\)
-
-       //Lift direction is orthogonal to delta, in the delta-normal plane. Its length is \(\left|n\right|\cdot\left|d\right|\)
-       \(\Lrg{ l_{dir} = \frac{\left( d \times n\right) \times d}{\left|d \right|} }\)
-
-       //Calculate the lift and drag impulse
-       //The lift is at its maximum when \(d\) is at an \(45^\circ\) angle to the triangle
-       //We use \(\sin\left(\theta\right)\cdot\cos\left(\theta\right) = \frac{1}{2}\sin\left(2\cdot \theta\right)\) to calculate this
-       \(i_{lift} = c_{lift} \cdot \cos\left(\theta\right) \cdot \sin\left(\theta\right) \cdot l_{dir} \)
-       \(i_{drag} = c_{drag} \cdot \left|\cos\left(\theta\right)\right| \cdot a \cdot d \)
-       //\(c_{lift} \) and \(c_{drag}\) are the lift and drag coefficients
-       //\(c_{drag}\) should be set to compensate for the double area in \(a\)
-
-       //combined impulse
-       \(\Lrg{ i =
-               \begin{cases}
-               \epsilon &lt; \left|d\right|^2,&amp; 0\\
-               \text{else},&amp; i_{lift} + i_{drag}
-               \end{cases}
-       }\)
-
-       //apply impulses to the particle positions
-       for each particle \(j = \left\{ 0, 1, 2 \right\} \)
-               \(c_j = c_j - i \cdot m^{-1}_j \)</pre>
-</div>
-<p>Note that when we combine the impulses we check if \(\left|d\right|\) is too small as this causes instabilities due to float division inaccuracies.
-This can cause different drag and lift behavior depending on the time step size (or solver frequency).
-Smaller time steps result in smaller position deltas which reach the \(\epsilon\) threshold sooner.
-This results in less drag/lift at small time steps (high solver frequencies) for slow moving particles.</p>
-</div>
-<div class="section" id="distance-constraints">
-<h2>Distance constraints<a class="headerlink" href="#distance-constraints" title="Permalink to this headline">¶</a></h2>
-<p>A distance constraint can limit the movement of a particle to the volume of a sphere.
-The constraints are specified with an array of 4 dimensional vectors (physx::PxVec4) where the x, y, z elements define the center and w the radius of the sphere.</p>
-<p>The constraints are interpolated between the start and target spheres if both are given.</p>
-<p>The constrainMotion() function in the solver is responsible for enforcing these constraints.
-The following pseudo code describes how this is implemented:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">delta</span> <span class="o">=</span> <span class="n">sphere_center</span> <span class="o">-</span> <span class="n">particle_position</span>
-<span class="n">sqrLength</span> <span class="o">=</span> <span class="n">epsilon</span> <span class="o">+</span> <span class="o">|</span><span class="n">delta</span><span class="o">|^</span><span class="mi">2</span>
-<span class="n">radius</span> <span class="o">=</span> <span class="n">max</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sphere_radius</span> <span class="o">*</span> <span class="n">scale</span> <span class="o">+</span> <span class="n">bias</span><span class="p">)</span>
-<span class="n">slack</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">radius</span> <span class="o">/</span> <span class="n">sqrt</span><span class="p">{</span><span class="n">sqrLength</span><span class="p">}</span>
-
-<span class="k">if</span><span class="p">(</span><span class="n">slack</span><span class="o">&gt;</span><span class="mi">0</span><span class="p">)</span>
-<span class="p">{</span>
-   <span class="k">if</span><span class="p">(</span><span class="n">radius</span> <span class="o">&lt;=</span> <span class="mi">0</span><span class="p">)</span>
-      <span class="n">particle_invMass</span><span class="p">.</span><span class="n">w</span> <span class="o">=</span> <span class="mi">0</span> <span class="c1">//Set the inverse mass to 0 if we are constrained to a zero radius sphere</span>
-   <span class="n">slack</span> <span class="o">=</span> <span class="n">slack</span> <span class="o">*</span> <span class="n">stiffness</span>
-   <span class="n">particle</span><span class="p">.</span><span class="n">xyz</span> <span class="o">+=</span> <span class="n">delta</span> <span class="o">*</span> <span class="n">slack</span>
-<span class="p">}</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="tether-constraints">
-<h2>Tether constraints<a class="headerlink" href="#tether-constraints" title="Permalink to this headline">¶</a></h2>
-<p>Tether constraints help with reducing the stretchiness of the cloth without increasing the solver iteration count.
-This is done by adding additional max distance constraints connecting simulated particles with their nearest fixed particle(s).
-The tether constraints are stored as an index &amp; length pair.
-The array of constraints has a multiple of particle count elements.
-The constraints in the array are stored in order so that the first particle of the constraint is element%numParticles.
-The index stored in the constraint defines the other (anchor) particle of the constraint.</p>
-<p>The constraint for one particle is solved as follows:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">offset</span> <span class="o">=</span> <span class="mi">0</span>
-<span class="k">for</span> <span class="n">each</span> <span class="n">tether</span> <span class="n">connecting</span> <span class="n">pb</span>
-    <span class="c1">//pa is the anchor particle</span>
-    <span class="n">delta</span> <span class="o">=</span> <span class="n">pa</span> <span class="o">-</span> <span class="n">pb</span>
-    <span class="n">radius</span> <span class="o">=</span> <span class="n">tetherLength</span> <span class="o">*</span> <span class="n">scale</span>
-    <span class="n">slack</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">radius</span> <span class="o">/</span> <span class="p">(</span><span class="o">|</span><span class="n">delta</span><span class="o">|</span> <span class="o">+</span> <span class="n">epsilon</span><span class="p">)</span>
-    <span class="n">offset</span> <span class="o">+=</span> <span class="n">delta</span> <span class="o">*</span> <span class="n">max</span><span class="p">(</span><span class="n">slack</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
-<span class="n">pb</span> <span class="o">+=</span> <span class="n">offset</span> <span class="o">*</span> <span class="n">stiffness</span>
-</pre></div>
-</div>
-<p>The stiffness is calculated as follows:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">stiffness</span> <span class="o">=</span> <span class="n">tetherConstraintStiffness</span> <span class="o">*</span> <span class="n">numParticles</span> <span class="o">/</span> <span class="n">numTethers</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="edge-constraints">
-<h2>Edge constraints<a class="headerlink" href="#edge-constraints" title="Permalink to this headline">¶</a></h2>
-<p>Algorithm:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="n">r</span> <span class="o">=</span> <span class="n">restlength</span>
-<span class="n">pi</span> <span class="o">=</span> <span class="n">particle</span> <span class="n">i</span>
-<span class="n">piw</span> <span class="o">=</span> <span class="n">inv</span> <span class="n">weight</span> <span class="n">of</span> <span class="n">particle</span> <span class="n">i</span>
-<span class="n">h</span> <span class="o">=</span> <span class="n">pb</span><span class="o">-</span><span class="n">pa</span>
-<span class="n">e2</span> <span class="o">=</span> <span class="n">epsilon</span> <span class="o">+</span> <span class="o">|</span><span class="n">h</span><span class="o">|^</span><span class="mi">2</span>
-<span class="n">er</span> <span class="o">=</span> <span class="n">r</span><span class="o">&gt;</span><span class="mi">0</span> <span class="o">?</span> <span class="p">(</span><span class="mi">1</span> <span class="o">-</span> <span class="n">r</span> <span class="o">/</span> <span class="n">sqrt</span><span class="p">{</span><span class="n">e2</span><span class="p">})</span> <span class="o">:</span> <span class="mi">0</span>
-
-<span class="k">if</span><span class="p">(</span><span class="n">useMultiplier</span><span class="p">)</span>
-<span class="p">{</span>
-    <span class="c1">//from PhaseConfig.h cloth::transform</span>
-    <span class="n">multiplierC</span> <span class="o">=</span> <span class="n">log2</span><span class="p">(</span><span class="n">stiffnessMultiplier</span><span class="p">)</span>
-    <span class="n">compressionLimitC</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">compressionLimit</span>
-    <span class="n">strechLimitC</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">stretchLimit</span>
-    <span class="n">er</span> <span class="o">-=</span> <span class="n">multiplierC</span> <span class="o">*</span> <span class="n">max</span><span class="p">(</span><span class="n">compressionLimitC</span><span class="p">,</span> <span class="n">min</span><span class="p">(</span><span class="n">er</span><span class="p">,</span> <span class="n">stretchLimitC</span><span class="p">))</span>
-<span class="p">}</span>
-
-<span class="n">stiffnessExponent</span> <span class="o">=</span> <span class="n">stiffnessFrequency</span> <span class="o">*</span> <span class="n">dt</span><span class="o">/</span><span class="n">iterations</span>
-<span class="n">stiffness</span> <span class="o">=</span> <span class="n">log2</span><span class="p">(</span><span class="mi">1</span><span class="o">-</span><span class="n">stiffness</span><span class="p">)</span> <span class="c1">//check when this happens //from PhaseConfig.h cloth::transform</span>
-<span class="n">stiffnessC</span> <span class="o">=</span> <span class="mi">1</span><span class="o">-</span><span class="mi">2</span><span class="o">^</span><span class="p">{</span><span class="n">stiffness</span> <span class="o">*</span> <span class="n">stiffnessExponent</span><span class="p">}</span>
-<span class="n">ex</span> <span class="o">=</span> <span class="n">er</span> <span class="o">*</span> <span class="n">stiffnessC</span> <span class="o">/</span> <span class="p">(</span><span class="n">pbw</span><span class="o">+</span><span class="n">paw</span><span class="p">)</span>
-
-<span class="n">pa</span> <span class="o">=</span> <span class="n">pa</span> <span class="o">+</span> <span class="n">h</span><span class="o">*</span><span class="n">ex</span> <span class="o">*</span> <span class="n">paw</span>
-<span class="n">pb</span> <span class="o">=</span> <span class="n">pb</span> <span class="o">-</span> <span class="n">h</span><span class="o">*</span><span class="n">ex</span> <span class="o">*</span> <span class="n">pbw</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="separation-constraints">
-<h2>Separation constraints<a class="headerlink" href="#separation-constraints" title="Permalink to this headline">¶</a></h2>
-<p>Separation constraints do exactly the opposite of distance constraints.
-These constraints ensure that the particles remain outside the defined spheres.</p>
-<p>The constraints are interpolated between the start and target spheres if both are given.</p>
-<p>The constrainSeparation() function in the solver is responsible for enforcing these constraints.
-Solving a single constraint is done as follows:</p>
-<div class="highlight-c++"><div class="highlight"><pre><span class="c1">//p is the particle position</span>
-<span class="c1">//c is the sphere center</span>
-<span class="c1">//r is the sphere radius</span>
-<span class="n">d</span> <span class="o">=</span> <span class="n">c</span><span class="o">-</span><span class="n">p</span>
-<span class="n">l</span> <span class="o">=</span> <span class="o">|</span><span class="n">d</span><span class="o">|</span>
-<span class="n">slack</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">-</span> <span class="n">r</span><span class="o">/</span><span class="n">l</span>
-<span class="k">if</span><span class="p">(</span><span class="n">slack</span> <span class="o">&lt;</span> <span class="mi">0</span><span class="p">)</span>
-    <span class="n">p</span> <span class="o">+=</span> <span class="n">d</span> <span class="o">*</span> <span class="n">slack</span>
-</pre></div>
-</div>
-</div>
-<div class="section" id="fabric-data-structure">
-<h2>Fabric data structure<a class="headerlink" href="#fabric-data-structure" title="Permalink to this headline">¶</a></h2>
-<p>The fabric data structure contains the constraint information that can be reused by multiple cloth instances.
-The constraints are divided in different phases.
-Each phase usually contains a different type of constraints such as (horizontal/vertical) stretching, searing, bending constraints.</p>
-<p>mPhases contains indices indicating which set from mSets belongs to a phase.</p>
-<p>mSets contains a list of start (and end) indices for mRestvalues and mIndices (if multiplied by 2).
-The first rest value of set s is mRestvalues[mSets[s]] and the last is mRestvalues[mSets[s+1]-1].</p>
-<p>mRestvalues contains the rest lengths / edge lengths of the constraints.</p>
-<p>mIndices contains pairs of indices connected by a constraint. (mIndices.size()*2 == mRestvalues.size())</p>
-</div>
-</div>
-
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-  <h3><a href="../NvCloth.html">Table Of Contents</a></h3>
-  <ul>
-<li><a class="reference internal" href="#">Internal solver function/algorithm documentation</a><ul>
-<li><a class="reference internal" href="#overview">Overview</a></li>
-<li><a class="reference internal" href="#particle-invmass-w-component">Particle invMass w component</a></li>
-<li><a class="reference internal" href="#slack">Slack</a></li>
-<li><a class="reference internal" href="#integration">Integration</a></li>
-<li><a class="reference internal" href="#wind-simulation">Wind simulation</a></li>
-<li><a class="reference internal" href="#distance-constraints">Distance constraints</a></li>
-<li><a class="reference internal" href="#tether-constraints">Tether constraints</a></li>
-<li><a class="reference internal" href="#edge-constraints">Edge constraints</a></li>
-<li><a class="reference internal" href="#separation-constraints">Separation constraints</a></li>
-<li><a class="reference internal" href="#fabric-data-structure">Fabric data structure</a></li>
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author	Marijn Tamis <[email protected]>	2017-04-28 14:19:07 +0200
committer	Marijn Tamis <[email protected]>	2017-04-28 14:19:07 +0200
commit	b350eb5f4d44e8448115796144375d79438d74ae (patch)
tree	8e102e8c28f45a1b87bd335ceee4f33c3d4ee7c2 /NvCloth/docs/documentation/Solver
parent	Add visual samples. (diff)
download	nvcloth-b350eb5f4d44e8448115796144375d79438d74ae.tar.xz nvcloth-b350eb5f4d44e8448115796144375d79438d74ae.zip