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Date: Mon, 16 Dec 1996 22:09:21 GMTServer: NCSA/1.5Content-type: text/htmlLast-modified: Wed, 13 Mar 1996 13:51:25 GMTContent-length: 5653<html><head><title>CS418 Lab 10</title></head><body><h2> <!WA0><!WA0><!WA0><!WA0><img src="http://www.tc.cornell.edu/Visualization/Education/cs418/gifs/teapot.thumb.gif">CS 418: Laboratory 10</h2> <h2> Physically Based Animation</h2><b> Introduction. </b><p>In this lab you will use physical (i.e. forces and accelerations)descriptions of processes to animate objects. There are several good reasons why you may want to compute motion of objectsbased on forces, rather than attempt a kinematic description of object motion.<ul><li> It is often easier to write an expression for the forces on an object(a differential equation) than it is to directly describe the motion.<li> Dynamic systems based on forces evolve "automatically" so than the motionis physically correct (given the correct equations). This automatic behaviorrelieves the animator of attention to lots of boring detail.<li> For chaotic systems it is impossible to write a kinematic description.</ul>Refer to the section on<!WA1><!WA1><!WA1><!WA1><ahref="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/dynamics.html"> dynamics </a> in the CS 417 page for more information about solving dynamic systems. Three examples are shown here of systemswhich would be difficult or impossible to animate by manual kinematicdescription.<ul> <li> <!WA2><!WA2><!WA2><!WA2><a href="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/dynamics.3body.mpg"> Three-body gravitation </a> <li> <!WA3><!WA3><!WA3><!WA3><a href="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/dynamics.WaterWave.mpg"> Water waves </a> <li> <!WA4><!WA4><!WA4><!WA4><a href="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/dynamics.billards.mpg"> Billards impact system </a></ul><b><hr>Assignment</b><p>Download:<ul><li> <!WA5><!WA5><!WA5><!WA5><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/labs/NbodyGravity.net"> NbodyGravity.net </a><li> <!WA6><!WA6><!WA6><!WA6><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/labs/NbodyGravity.cfg"> NbodyGravity.cfg </a><p><li> <!WA7><!WA7><!WA7><!WA7><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/labs/2DLinearWave.net"> 2DLinearWave.net </a><li> <!WA8><!WA8><!WA8><!WA8><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/labs/2DLinearWave.cfg"> 2DLinearWave.cfg </a><p><li> load macros and move to your .DXmacros directory <ul> <li> <!WA9><!WA9><!WA9><!WA9><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/labs/NbodyGmacro.net"> NbodyGmacro.net </a> </ul></ul><p><blink> Bug as of 3/4/96 </blink> <br>After you donwload the NbodyGmacro.net, open it and remove the Set module, then replace it with a new Set module, then reconnect it and save it. (The internal stateof the module seems to be messed up).<p>Execute the programs to understand their behavior, then modify them asfollows:<ul><li> Modify the NbodyGravity.net to allow other force laws besides inverse square.Provide an interactor to set the exponent on the law from inverse firstpower to inverse fourth power. Can you make a stable orbit with just twogravitating bodies for inverse first power or inverse third power forcelaws?<p><li> Modify the linear wave equation given in program 2DLinearWave.netto simulate water by making the accelerationproportional to depth. Refer to the<!WA10><!WA10><!WA10><!WA10><ahref="http://www.tc.cornell.edu/Visualization/Education/cs417/SECTIONS/dynamics.html"> dynamics</a> section for more information on waterwaves.Make the 2D function which represents the bottomof the region containing the water have some variation with position, perhapsa gaussian hillock:<p><b>Note correction on 3/13/96.</b> A missing minus sign was added.<p><code> z = -1 + 0.7*exp(-((x-0.5)^2 + (y-0.5)^2)/0.2) </code> <p>When the modified program is running correctly, the water wave should slow downover the bump, and will bounce off the bump if it is above the surface. <p><li> Modify the water-wave program you just wrote to simulate acannon firing a ball through the air and into water where it starts awave. Use a Euler integrator for the ball (and the given Verlet integrator forthe water). The ball should have initial conditionsof position corresponding to the muzzle of the cannon and a velocityconsistent with the cannon's altitude (angle with the horizontal)and azimuth (horizontal direction).You should be able to set the altitude and azimuth of the cannonvia interactors, which means you will have to detect where and when theball hits the water surface (which is flat until the ball hits it). Youwill need to figure out how to notify the water simulation that the ballhit, perhaps by adding a sudden velocity to the water where the ballhit. There should be interactors to set theforce of gravity on the ball, <code>g</code> and the air drag coefficient, <code>r</code>.<p>For the ball assume that: <p><code>ax = - r*vx <p>ay = - r*vy <p>az = -g - r*vz<p></code>where <code> [vx, vy, vz] </code>are the components of the velocity, and <code>[ax, ay, az]</code> the components of the accelaration.</ul><hr>Be prepared to demo the two programs in section. You will also need to demonstrate <!WA11><!WA11><!WA11><!WA11><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/MPEG/mpeg.html"> mpeg </a> movies of final results including:<ul><li> An orbit (if any), in an inverse first power field.<li> One paticular cannon shot into the water.</ul><p>You should be able to explain your programs. You should usetransmitters/receivers, macros, and comments in the "Notation" field of each moduleso that you and the grader can understand the program. Control panels, if any,should be well organized, labeled, and with the appropriate numeric ranges.<p><!WA12><!WA12><!WA12><!WA12><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/student.1996.gifs/lab10.96results.html">Some results from 1996. </a><p>The<!WA13><!WA13><!WA13><!WA13><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/GradeGuides/Lab10.grade.ps"> Lab 10 grading guide </a>will be filled out by a consultant during section to evaluate your work.<p><hr><!WA14><!WA14><!WA14><!WA14><img src="http://www.tc.cornell.edu/Visualization/Education/cs418/gifs/leftarrow.icon.gif">Back to <!WA15><!WA15><!WA15><!WA15><a href="http://www.tc.cornell.edu/Visualization/Education/cs418/index.html">Main Page</a> <P><hr>Last modified, 10/20/95, B. Land.<! Revision history: Original document: Land 10/95><br><!WA16><!WA16><!WA16><!WA16><IMG SRC="http://www.tc.cornell.edu/copyright.xbm"><!WA17><!WA17><!WA17><!WA17><A HREF="http://www.tc.cornell.edu/ctcCopyright.html"> <i>Copyright Statement </I></A></body> </html>⌨️ 快捷键说明
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