1 / 12

Static and dynamic surfaces representation

Learn to visualize lines, surfaces, and 3-D curves using MATLAB, Mathematica, and DPGRAPH. Understand implicit expressions, transparencies, and real-time scrolling for effective mathematical representation.

hunnicutt
Download Presentation

Static and dynamic surfaces representation

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Gliwice July 25-29, 2005 Static and dynamic surfaces representation • Matilde P. Legua • Jose A. Moraño • Luis M. Sánchez-Ruiz

  2. Introduction • Visualization of lines and surfaces • Geometrical application problems • To teach mathematical concepts when we are working with scalar fields • To help to locate the regions which we should pay special attention • The aim is to take advantages of capabilities of commonly used mathematical software to get the proper representation

  3. Surfaces representation • Implicit expressions & Transparencies • Surfaces defined by inequalities • Real Time scrolling • Graphs in movement • Parametric surfaces • More about surfaces representation • 3-D curves

  4. Usual software • DPGRAPH • DERIVE • MATLAB • MATHEMATICA

  5. Implicit expressions & Transparencies Visualize Intersections: • DERIVE • - Explicit expressions • Transparencies: See_through() • DPGRAPH • - Implicit expressions • Gradual Transparencies

  6. Surfaces defined by inequalities Defined regions: • DERIVE • Several surfaces but without inequalities • Other possibilities: Revolution, lines, ... DPGRAPH -  is & between inequalities RevY_Iplot(x=sin(y/2) z=3, y, -PI, PI)

  7. Real time scrolling Meaning of parameters: DPGRAPH: Scroll bar modifies the parameter in real time DERIVE: Can use Vector( ) command. VECTOR(RevZ_IPlot(z = 5(1-x^2/k^2)^(1/2)  y=0, 0  x  k), k,1, 5)

  8. Graphs in movement Meaning of parameters by dynamic representations: DPGRAPH: Including another dimension (time) DERIVE:time also exists

  9. Parametric surfaces Several coordinate systems: Rectangular, cylindrical, spherical, ... DPGRAPH: Trace a graph only over a rectangle RECTANGULAR (u,v,–2*COS(1.75*u)+SIN(v)) It can plot surfaces whose domain is not a rectangle RECTANGULAR (3/4*(v-u),1/4*(u+3*v),3-v/2+u/6) DERIVE: It has more types of coordinate system

  10. More about surfaces representation Matlab: Several interesting commands • mesh, surf • meshc and surfc (with level lines) • Subplot (distributing graphs) • Using OpenGL renderer (transparencies) • MOVIE (dynamical graphs) • As a drawback (Surfaces in implicit form are not admitted) Mathematica is a good tool also • Plot3D, ParametricPlot3D • Hidden Surface (transparencies) • Animate (Variation on a parameter) or ShowAnimation (sequence of graphs)

  11. 3D-Curves DPGRAPH: Parametrical coordinates allow visualize 3D curves RECTANGULAR (2*SIN(4*u),2*COS(4*u),u) DERIVE, MATLAB and MATHEMATICA provide similar graphs

  12. Conclusion • Sofisticated mathematical software should get better results however DPGRAPH seems to be more practical and easier when we are • working with implicit forms • building dynamic surfaces • getting transparencies • needing memory requirements • We must have very clear that it is not a CAS

More Related