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Plot 3D surfaces

, 21 Feb 2007
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Simply render a 3D surface on your screen without OpenGL/DirectX.
Screenshot - Plot3D_sample1.png

Introduction

This article describes a simple method of rendering 3D surfaces on a 2D plane. It doesn't use OpenGL or DirectX or stuff like that. It just utilizes the power of the CPU. Simplicity has, of course, its price - the rendering process isn't as fast as when using hardware acceleration.

Its application varies from simply admiring beautiful 3D surfaces to data visualization purposes, to stuff whatever one needs. I've used it in programs written for courses of Optimization Methods, Identification, Calculus (Mathematical Analysis), and Dimensional Analysis.

Properties

  • Density - Size of the spanning mesh.
  • PenColor - Color of the drawing pen. Used to draw meshes.
  • StartPoint - Plotting start point.
  • EndPoint - Plotting end point.
  • Function - Function used to calculate surface vertices.
  • ColorSchema - Color schema assigned to mesh.

Methods

  • ReCalculateTransformationsCoeficients - Recalculates transformations' coefficients on the basis of new parameters.
  • Project - Performs projection. Calculates screen coordinates for the 3D point.
  • RenderSurface - Main method. Render the surface on given graphics.

Points of Interest

Additional classes ColorSchema and CompiledFunction are interesting parts of the code. The first one encapsulates an array of Color entries. It has some predefined color palettes. The other one compiles a given formula to a function delegate, providing simple parser services.

Usage

Surface3DRenderer sr = new Surface3DRenderer(70, 35, 40, 
                       0, 0, ClientRectangle.Width, 
                       ClientRectangle.Height, 0.5, 0, 0);
//new hue-based palette
sr.ColorSchema = new ColorSchema(120);
//enter your function here        
sr.SetFunction("sin(x1)*cos(x2)/(sqrt(sqrt(x1*x1+x2*x2))+1)*10");

Use this to actually render something:

sr.RenderSurface(e.Graphics);

And this, whenever plotting area size changes:

sr.ReCalculateTransformationsCoeficients(70, 35, 40, 0, 0, 
     ClientRectangle.Width, ClientRectangle.Height, 0.5, 0, 0);

Copyright

History

  • 22.02.2007 - first version.
  • 23.02.2007 - sample images added.

Sample (application)

Below, I'm publishing screenshots from an application that was written for my academic course of Optimization Methods (finding the minimum/maximum of functions). Labels are in Polish, but I hope that they are self-explaining.

Screenshot - wykres.png

Entering the formula:

Screenshot - wzor.png

Finding functions' minimum using the Greatest Slope method:

Screenshot - tabelka.png

License

This article has no explicit license attached to it but may contain usage terms in the article text or the download files themselves. If in doubt please contact the author via the discussion board below.

A list of licenses authors might use can be found here

About the Author

Michal Brylka
Architect Nokia Siemens Networks
Poland Poland
Michał is C# and whole .NET enthusiast. He graduated from computer science MSc studies at Wroclaw University of Technology, Poland.
 
He is interested in photography and diving. He is member of PADI, currently with divemaster certificate.

His favorite movies are Matrix, Amélie(Le Fabuleux Destin d'Amélie Poulain), Stargate SG-1 TV Serie and comedies of Mel Brooks.
 
Michał lives in Wroclaw, Poland. To contact Michał, email him at michal.brylka[mail-'"at'"-sign]op.pl.

Comments and Discussions

 
Generalnice, may be just what i'm after.. Pinmemberibyk301-May-13 6:43 
SuggestionRe: nice, may be just what i'm after.. Pinmemberibyk303-May-13 4:57 
GeneralMy vote of 5 Pinmemberibyk301-May-13 6:28 
GeneralMy vote of 5 Pinmembervictorbos4-Apr-13 14:18 
Nice clean working code. Superb
QuestionHow to achieve same grid effect as on second screenshot Pinmemberapaka31-Oct-12 22:14 
Questionsr is null before initialization in mono Pinmemberj1s1e129-Oct-12 17:55 
QuestionAdding mouse interaction Pinmemberxfx27-Mar-12 20:06 
SuggestionRe: Adding mouse interaction PinmemberMichal Brylka5-Apr-12 1:27 
GeneralMy vote of 5 Pinmembermanoj kumar choubey26-Feb-12 21:50 
QuestionWhile obsX smaller than 0 Pinmembertransparency5-Apr-11 23:13 
Generaluser interaction Pinmembernow7864-Apr-11 11:09 
GeneralExcellent library; license question Pinmembersirkne12322-Sep-09 8:35 
GeneralI can,t calculate the beginings coordinates of 3d plot Pinmemberartem0055-Apr-09 20:36 
GeneralRe: I can,t calculate the beginings coordinates of 3d plot PinmemberMichal Brylka2-Sep-09 9:14 
GeneralRe: I can,t calculate the beginings coordinates of 3d plot Pinmemberartem0053-Sep-09 4:51 
GeneralTransformations PinmemberLinuxman14-Jan-09 2:15 
QuestionQuestion about 3D graphic Pinmemberjohndoelee1-Apr-08 5:30 
GeneralColor Schema PinmemberPaul Selormey25-May-07 22:15 
GeneralRe: Color Schema PinmemberMichal Brylka26-May-07 1:31 
GeneralRe: Color Schema PinmemberPaul Selormey26-May-07 2:51 
GeneralRe: Color Schema PinmemberMichal Brylka26-May-07 8:29 
GeneralRe: Color Schema PinmemberPaul Selormey26-May-07 9:51 
GeneralRe: Color Schema PinmemberMichal Brylka26-May-07 10:51 
GeneralRe: Color Schema PinmemberPaul Selormey27-May-07 0:30 
GeneralRe: Color Schema PinmemberMichal Brylka27-May-07 2:12 

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