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<html><head><meta http-equiv="Content-Type" content="text/html; charset=ISO-8859-1"><title>4.2. Simulation</title><link rel="stylesheet" href="megapov.css" type="text/css"><meta name="generator" content="DocBook XSL Stylesheets V1.65.1"><link rel="home" href="index.html" title="MegaPOV Documentation"><link rel="up" href="tutorials.html" title="Chapter 4. Tutorials"><link rel="previous" href="tutorials.html" title="Chapter 4. Tutorials"><link rel="next" href="tutorials_hdri.html" title="4.3. HDRI (High dynamic range illumination)"></head><body bgcolor="white" text="black" link="#0000FF" vlink="#840084" alink="#0000FF"><div class="navheader"><table width="100%" summary="Navigation header"><tr><th colspan="3" align="center">4.2. Simulation</th></tr><tr><td width="20%" align="left"><a accesskey="p" href="tutorials.html">Prev</a> </td><th width="60%" align="center">Chapter 4. Tutorials</th><td width="20%" align="right"> <a accesskey="n" href="tutorials_hdri.html">Next</a></td></tr></table><hr></div><div class="section" lang="en"><div class="titlepage"><div><div><h2 class="title" style="clear: both"><a name="tutorials_simulation"></a>4.2. Simulation</h2></div></div><div></div></div><div class="section" lang="en"><div class="titlepage"><div><div><h3 class="title"><a name="mechsim_tutorial"></a>4.2.1. Mechanics simulation tutorial</h3></div><div><div class="author"><h3 class="author"><span class="firstname">Christoph</span> <span class="surname">Hormann</span></h3></div></div></div><div></div></div><p>
    This part of the MegaPOV documentation gives
    a short practical introduction into using
    the mechanics simulation patch and describes
    some simple simulations step by step.
  </p><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_mass"></a>4.2.1.1. mass movement</h4></div></div><div></div></div><p>
      The simplest thing that can be simulated with the mechanics simulation patch
      is the movement
      of individual point masses.  Their movement under the influence of gravity
      and environment objects is handled in this part.
    </p><p>We start with a simple scene setup:</p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial01.pov" target="_top"><tt class="filename">tutorial01.pov</tt></a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial01.png"></div></div><p>
    </p><p>
      To simulate the movement of a single mass we add the following to the
      <tt class="function">global_settings{}</tt>:
    </p><div class="informalexample"><pre class="programlisting">mechsim {		
  gravity &lt;0, 0, -9.81&gt;
  method 1

  environment {
    object plane { z, 0 }
    damping 0.9
    friction 0.1
    method 2
  }

  time_step (1/30)/300
  step_count 300
		
  #if (frame_number=1)
    topology {
      mass { &lt;-2.8, -8.0, 0.9&gt;, &lt;2, 5, 0&gt;, 0.1 density 5000 }
      save_file "tut02.dat"
    }
  #else
    topology {
      load_file "tut02.dat"
      save_file "tut02.dat"
    }
  #end
}</pre></div><p>
      The purpose of the individual lines of this block is the following:
    </p><p>
      <tt class="function">gravity &lt;0, 0, -9.81&gt;</tt> activates a standard gravity force in negative
      vertical direction.
    </p><p>
      <tt class="function">method 1</tt> selects simulation method 1 (Euler integration).
    </p><p>
      The <tt class="function">environment {}</tt> block contains the definition of
      the environment. It contains:
    </p><div class="itemizedlist"><ul type="disc"><li><p>
        <tt class="function">object plane { z, 0 }</tt> - the environment object,
        a plane like seen in the image.
      </p></li><li><p>
        <tt class="function">damping 0.9</tt> - a damping factor decreasing the
        velocity perpendicular to the surface to 90% during every collision.
      </p></li><li><p>
        <tt class="function">friction 0.1</tt> - a friction factor decreasing the
        velocity tangential to the surface by 10% during every collision.
      </p></li><li><p>
        <tt class="function">method 2</tt> - activates method 2 collision calculation
        (impact law based collision).
      </p></li></ul></div><p>
      The next two lines specify the timing of the simulation:
    </p><div class="itemizedlist"><ul type="disc"><li><p>
        <tt class="function">step_count 300</tt> - makes MegaPOV calculate 300 simulation steps
        per frame.
      </p></li><li><p>
        <tt class="function">time_step (1/30)/300</tt> - sets the duration of each step
        appropriate for a 30 fps animation.
      </p></li></ul></div><p>
      Finding the right step size is probably something most difficult for the
      beginner.  A smaller step size generally leads to more accurate results.  Usually
      the step size has to be below a certain value depending on the other simulation
      settings to get usable results, but it is not always obvious if some strange result
      is due to large time steps.  High stiffness values in environments, collision and
      connections usually require smaller time steps.  If you experience unexpected results
      it is often worth trying to decrease the step size and see if problems vanish.
    </p><p>
      There is also the possibility to use adaptive time stepping that will be introduced in 
      the next part of this tutorial.
    </p><p>
      What follows is an <tt class="function">#if</tt> conditional.  It makes
      sure the mass is generated in the first frame and saved to the file
      while the following frames load and save the simulation data.
    </p><p>The first part contains statements for the first frame:</p><p>
      The <tt class="function">topology{}</tt> block contains a singular <tt class="function">mass{}</tt>
      section.  It contains:
    </p><div class="itemizedlist"><ul type="disc"><li><p>
        <tt class="function">&lt;-2.8, -8.0, 0.9&gt;</tt> - the starting position of the mass.
      </p></li><li><p>
        <tt class="function">&lt;2, 5, 0&gt;</tt> - the initial velocity of the mass.
      </p></li><li><p>
        <tt class="function">0.1</tt> - the radius of the mass.
      </p></li><li><p>
        <tt class="function">density 5000</tt> - the density of the mass (in <tt class="function">kg/m³</tt>).
      </p></li></ul></div><p>
      The <tt class="function">save_file</tt> statement finally saves this mass to a file.
    </p><p>The second part contains the variant for the subsequent frames.</p><p>
      The <tt class="function">topology{}</tt> block here contains just <tt class="function">load_file</tt>
      and <tt class="function">save_file</tt> statements referring to the same file.  This makes
      MegaPOV load the old simulation data at the beginning, calculate the steps for
      the current frame and save to the same file afterwards.
    </p><p>
      To show the mass in the scene we can use a macro from the
      <tt class="filename"><tt class="filename">mechsim.inc</tt></tt>
      include file:
    </p><div class="informalexample"><pre class="programlisting"><tt class="function">#include</tt> "<tt class="filename">mechsim.inc</tt>"

MechSim_Show_All_Objects(-1, false, -1, "")</pre></div><p>
      The meaning of the parameters of this macro is described in
      <a href="mechsim.inc.html#mechsim_inc_MechSim_Show_All_Objects" title="3.4.4.2. MechSim_Show_All_Objects()">Section 3.4.4.2, &#8220;MechSim_Show_All_Objects()&#8221;</a>.
    </p><p>
      Now all we need to do is render the scene using the render options that
      can be found in the scene file comment and we get the following result:
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial02.pov" target="_top"><tt class="filename">tutorial02.pov</tt></a></li><li><a href="msim_tut/tutorial02.mpg" target="_top"><tt class="filename">tutorial02.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial02.png"></div></div><p>
    </p></div><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_coll"></a>4.2.1.2. collisions</h4></div></div><div></div></div><p>
      In the first part of the tutorial we have handled masses and their movement under
      the influence of gravity and the constraints of the environment.  If several masses
      exist in the simulation collisions between have to be taken into account.
    </p><p>
      For turning collision calculation on the following block is added to the
      <tt class="function">mechsim{}</tt> section:
    </p><div class="informalexample"><pre class="programlisting">collision {
  1, 0, 0
  stiffness 60000
  damping 4000
}</pre></div><p>
      The first three numbers tell MegaPOV which collision to calculate.  For details
      see <a href="global_settings.html#mechsim_collision" title="2.7.4.1.3. The collision settings">Section 2.7.4.1.3, &#8220;The collision settings&#8221;</a>.  The numbers used here
      turn calculation on for all mass-mass collisions.
    </p><p>
      <tt class="function">stiffness</tt> (unit <tt class="function">kg/s²</tt>) and
      <tt class="function">damping</tt> (unit <tt class="function">kg/s</tt>) influence
      how the masses interact.
    </p><p>
      Another change made in this tutorial step is changing the environment
      to function based calculations.  This usually leads to more accurate environment
      collisions, especially with more complex geometries.
    </p><p>
      Defining the environment as a function is fairy easy with the
      <a href="http://www.tu-bs.de/~y0013390/pov/ic/" target="_top">IsoCSG library</a>.
      The definition in this case looks like:
    </p><div class="informalexample"><pre class="programlisting">#include "iso_csg.inc"

#declare fn_Env=
IC_Merge5(
  IC_Plane(z, 0),
  IC_Box(&lt; 1.7,-1.7,-1.0&gt;, &lt; 1.5,1.7,0.5&gt;),
  IC_Box(&lt;-1.7,-1.7,-1.0&gt;, &lt;-1.5,1.7,0.5&gt;),
  IC_Box(&lt;-1.7, 1.7,-1.0&gt;, &lt;1.7, 1.5,0.5&gt;),
  IC_Box(&lt;-1.7,-1.7,-1.0&gt;, &lt;1.7,-1.5,0.5&gt;)
)</pre></div><p>
      Note that the <tt class="function">stiffness</tt>, <tt class="function">damping</tt> and
      <tt class="function">friction</tt> parameters in the environment now have the same meaning
      as in the collision settings because it uses calculation method 1 (force based
      environment collisions).
    </p><p>
      Force based environment collisions lead to a more realistic simulation of the
      interaction of the masses with the environment since the movement of the masses does
      not abruptly change.  Using this method is necessary for all higher order integration
      methods which will be introduced later.
    </p><p>
      This scene also adds new masses during the animation.  This is achieved by adding
      the following code to the <tt class="function">topology{}</tt> section:
    </p><div class="informalexample"><pre class="programlisting">#if (mod(frame_number, 6)=5)
  mass { &lt; 1.3,-1.55,0.8&gt;, &lt;-0.2, 5, 0&gt;, 0.18 density 5000 }
#end</pre></div><p>
      It means that in every sixth frame a new mass is added at the starting
      position with the same starting velocity as the first mass.
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial03.pov" target="_top"><tt class="filename">tutorial03.pov</tt></a></li><li><a href="msim_tut/tutorial03.mpg" target="_top"><tt class="filename">tutorial03.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial03.png"></div></div><p>
    </p></div><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_con"></a>4.2.1.3. connections</h4></div></div><div></div></div><p>
      Apart from masses there is another important element that can be added to the
      <tt class="function">topology{}</tt> section: connections.  Connections can be seen as
      springs.  They connect two point masses and exert a force on them depending on the
      current distance of the masses compared to the relaxed length of the connection.
      In addition there is a damping property generating dissipative forces.
    </p><p>
      A <tt class="function">connection{}</tt> block is added to the
      <tt class="function">topology{}</tt> section like a mass:
    </p><div class="informalexample"><pre class="programlisting">connection { 0, 1 stiffness 50000 damping 2000 }</pre></div><p>It contains:</p><div class="itemizedlist"><ul type="disc"><li><p>
        <tt class="function">0</tt> - the index of the first mass connected.
      </p></li><li><p>
        <tt class="function">1</tt> - the index of the second mass connected.
      </p></li><li><p>
        <tt class="function">stiffness 50000</tt> - the stiffness of the connection (unit <tt class="function">kg/s²</tt>).
      </p></li><li><p>
        <tt class="function">damping 2000</tt> - the damping of the connection (unit <tt class="function">kg/s</tt>).
      </p></li></ul></div><p>
      if no <tt class="function">length</tt> is given the current
      distance of the masses is used.
    </p><p>
      The mass indices are counted in order of creation starting at zero.
      The three connected
      masses from the following scene are created with:
    </p><div class="informalexample"><pre class="programlisting">topology {
  mass { &lt;0, 0, 2.4&gt;, &lt;0, 0, 0&gt;, 0.1 density 5000 fixed on }
  mass { &lt;1, 0, 2.4&gt;, &lt;0, 0, 0&gt;, 0.1 density 5000 }
  mass { &lt;2, 0, 2.4&gt;, &lt;0, 0, 0.6&gt;, 0.15 density 5000 }
  connection { 0, 1 stiffness 50000 damping 2000 }
  connection { 1, 2 stiffness 50000 damping 2000 }
}</pre></div><p>
      The <tt class="function">fixed on</tt> in the first mass definition fixes the
      position of this mass.
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial04.pov" target="_top"><tt class="filename">tutorial04.pov</tt></a></li><li><a href="msim_tut/tutorial04.mpg" target="_top"><tt class="filename">tutorial04.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial04.png"></div></div><p>
    </p></div><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_grid"></a>4.2.1.4. grids</h4></div></div><div></div></div><p>
      With plenty of such connections we can form more complex shapes.
      The <tt class="filename">mechsim.inc</tt> include file
      (see <a href="mechsim.inc.html" title="3.4. The 'mechsim.inc' include file">Section 3.4, &#8220;The 'mechsim.inc' include file&#8221;</a>)
      contains several macros forming grids of masses and connections.
    </p><p>
      Placing the following in the <tt class="function">topology{}</tt> section generates a
      box-like grid of connected masses:
    </p><div class="informalexample"><pre class="programlisting">MechSim_Generate_Block(
  &lt;0, 0, 0&gt;, 0.07, 1500, 22000, 2000, true,
  &lt;-0.5, -2.75, 1.0&gt;, &lt;0.5, 2.75, 2.0&gt;, &lt;3, 12, 3&gt;, No_Trans, 3
)</pre></div><p>
      The meaning of the different parameters is described in
      <a href="mechsim.inc.html#mechsim_inc_MechSim_Generate_Block" title="3.4.5.11. MechSim_Generate_Block()">Section 3.4.5.11, &#8220;MechSim_Generate_Block()&#8221;</a>.
    </p><p>
      Apart from the grid macro we introduce a different simulation method in
      this scene.  <tt class="function">method 3</tt> uses adaptive time stepping.
      This means you don't need to specify a step size but instead specify how 
      accurate the simulation should be.  The <tt class="function">accuracy</tt>
      option takes two parameters: the maximum allowed local discretization
      error and the minimum step size to use.
    </p><p>
      Note that you might still need to specify an appropriate starting step size
      using <tt class="function">time_step</tt> - the default value might not be
      appropriate.
    </p><p>
      In addition to the accuracy settings the total time per frame is specified
      using the <tt class="function">time</tt> parameter.
    </p><p>
      The resulting animation shows a moving and deforming box geometry.
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial05.pov" target="_top"><tt class="filename">tutorial05.pov</tt></a></li><li><a href="msim_tut/tutorial05.mpg" target="_top"><tt class="filename">tutorial05.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial05.png"></div></div><p>
    </p><p>
      The <tt class="function">MechSim_Generate_Block()</tt> macro also generates faces for the
      outside surface of the box.  Faces are triangles each connecting three masses.  They
      can be used for collision calculations and for displaying the geometry as a mesh.
      The latter can be done easily by changing the parameters of the
      <tt class="function">MechSim_Show_All_Objects()</tt> macro:
    </p><div class="informalexample"><pre class="programlisting">MechSim_Show_All_Objects(-1, true, -1, "")</pre></div><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial06.pov" target="_top"><tt class="filename">tutorial06.pov</tt></a></li><li><a href="msim_tut/tutorial06.mpg" target="_top"><tt class="filename">tutorial06.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial06.png"></div></div><p>
    </p></div><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_patch"></a>4.2.1.5. patches</h4></div></div><div></div></div><p>
      Apart from 3D grids we of course can also create 2D rectangular patches.
      Such objects behave like cloth or foil and offer a very interesting field
      of simulation.
    </p><p>
      Like 3D grids rectangular patches can be created with macros from
      the <tt class="filename">mechsim.inc</tt> include file
      (see <a href="mechsim.inc.html" title="3.4. The 'mechsim.inc' include file">Section 3.4, &#8220;The 'mechsim.inc' include file&#8221;</a>):
    </p><div class="informalexample"><pre class="programlisting">MechSim_Generate_Patch_Std(
  &lt;0, 0, 0&gt;, 0.03, 8000, 10000, 0,
  true, &lt;0.055, 0.055&gt;, &lt;50, 50&gt;, Trans1, 2
)</pre></div><p>
      This creates a 50x50 masses patch, again movable with a
      <tt class="function">transform</tt>.  Description of the parameters can be found in
      <a href="mechsim.inc.html#mechsim_inc_MechSim_Generate_Patch_Std" title="3.4.5.15. MechSim_Generate_Patch_Std()">Section 3.4.5.15, &#8220;MechSim_Generate_Patch_Std()&#8221;</a>.
    </p><p>
      The following sample scene also uses a different simulation method than
      the previous scenes.  It is called gradient descent method. It does not integrate the
      equations of movement like the other methods but moves the masses directly according
      to the forces influencing them.  Inertia does not have effect with these method,
      therefore oscillations can't occur.  Still the step size has to be chosen small enough
      for accurate results.  The movement won't look very realistic in an animation but
      the final result can be used for a still render.  Another disadvantage is the lack
      of friction, therefore the patch slides off the sphere in the end.
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial07.pov" target="_top"><tt class="filename">tutorial07.pov</tt></a></li><li><a href="msim_tut/tutorial07.mpg" target="_top"><tt class="filename">tutorial07.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial07.png"></div></div><p>
    </p><p>
      There is also a specialized macro for generating a mesh from a patch topology
      including normal vectors and uv coordinates.  Rendering the previous topology with
      this macro results in the following picture:
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial08.pov" target="_top"><tt class="filename">tutorial08.pov</tt></a></li><li><a href="msim_tut/tutorial08.mpg" target="_top"><tt class="filename">tutorial08.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial08.png"></div></div><p>
    </p><p>
      There are a lot more aspects of the mechanics simulation patch that are not
      handled in this tutorial yet.  Reading the reference
      (see <a href="global_settings.html#mechsim" title="2.7.4. Mechanics simulation patch">Section 2.7.4, &#8220;Mechanics simulation patch&#8221;</a>) and
      <tt class="filename">mechsim.inc</tt> include file documentation
      (see <a href="mechsim.inc.html" title="3.4. The 'mechsim.inc' include file">Section 3.4, &#8220;The 'mechsim.inc' include file&#8221;</a>) should help learning
      about those things.  The sample scenes show several examples what
      the simulation system
      can be used for but there are a lot more possibilities.
    </p></div><div class="section" lang="en"><div class="titlepage"><div><div><h4 class="title"><a name="mechsim_tut_interaction"></a>4.2.1.6. mass interaction</h4></div></div><div></div></div><p>
      Masses can not only collide but also can interact in a freely definable way.
      This way you can simulate physical effect like electromagnetic fields and gravity.
    </p><p>
      Mass interaction is defined globally with the<tt class="function">interaction</tt> keyword
      in the <tt class="function">mechsim{}</tt> block.  For the inverse square law of gravity
      you for example could use the following setup:
    </p><div class="informalexample"><pre class="programlisting">// Gravitation constant: 6.672e-11 m^3*kg^-1*s^-2
#declare G=6.672e-11;

// Newton's law of gravitation
#declare fn_Gravity=
  function(x, y, z, dist, m1, m2) {
    (G*m1*m2)/(dist*dist)
  }

global_settings {
  mechsim {
    ...
    interaction {
      function(x, y, z, dist, m1, m2) { fn_Gravity(x, y, z, dist, m1, m2) }
    }
    ...
  }
}</pre></div><p>
      As you can see the interaction function has 6 parameters.  The first three
      are the usual coordinates so you can define an interactions that differs
      depending on the absolute position.  The last three are optional, the first 
      of them is the distance between the masses and the other two the masses
      of the two masses that interact.
    </p><p>
      The simulation system calls this function for every pair of masses in every 
      simulation step.  This can of course be quite slow with a lot of masses.
      But in this simple example we only want to simulate the movement of the earth
      around the sun which is done with the following topology definition:
    </p><div class="informalexample"><pre class="programlisting">#declare Mio_km=1.0e9;

topology {
  // Sun
  mass { &lt;0,0,0&gt;, &lt;0,0,0&gt;, 696.0e6 mass 1.99e30 }
  // Earth
  mass { &lt;149.6*Mio_km,0,0&gt;, &lt;0,29.8*1000,0&gt;, (6371.0)*1000 mass 5.97e24 }

  save_file "tut09.dat"
}</pre></div><p>
      Simulating this with 1 step per day is done with the following code:
    </p><div class="informalexample"><pre class="programlisting">step_count 2000

// 1 day per step
time_step (24*3600)/2000

topology {
  load_file "tut09.dat"
  save_file "tut09.dat"
}</pre></div><p>
      And results in the following movement.  The size of the sun and earth is of course
      strongly exaggerated.  You can find a more complex simulation of all the inner
      planets in the <tt class="filename">planets.pov</tt> sample scene.
    </p><div class="itemizedlist"><ul type="disc" compact><li><a href="msim_tut/tutorial09.pov" target="_top"><tt class="filename">tutorial09.pov</tt></a></li><li><a href="msim_tut/tutorial09.mpg" target="_top"><tt class="filename">tutorial09.mpg</tt> (mpeg, 320x240)</a></li></ul></div><p>
      </p><div class="informalfigure"><div><img src="img/tutorial09.png"></div></div><p>
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