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Mapping Images on Spherical Surfaces Using C#

, 9 Apr 2013
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Mapping images on spherical surfaces using C#

Introduction

This article describes how to map a flat 2D image (JPG, BMP, or GIF) on a sphere by using basic algebra.

The process is very simple where the x axis of the image will be mapped on sphere longitudes and the y axis of the image will be mapped on sphere latitudes.

The process of mapping is similar to proportion equations x-x0/y-y0 = px-x0/py-y0

public static double MapCoordinate(double i1, double i2, double w1,
    double w2, double p)
{
    return ((p - i1) / (i2 - i1)) * (w2 - w1) + w1;
}

Screenshot - worldmap4.gif
Original image

Screenshot - mapping.png
Resulting image

Background

A Sphere Can Be Represented by Spherical Coordinates in R3

  • radius
  • phi (latitude angle)
  • theta (longitude angle)

Image 2

  • Where radius is a constant, phi=[-PI/2,PI/2], and theta=[0,2*PI]

To Find the Cartesian Coordinates from Spherical Coordinates

  • x = radius * sin(phi) * cos(theta)
  • y = radius * sin(phi) * sin(theta)
  • z = radius * cos(theta)
double phi0 = 0.0;
double phi1 = Math.PI;
double theta0 = 0.0;
double theta1 = 2.0*Math.PI;

The Code

At first we code the image loading

System.Drawing.Image image1 = new Bitmap(Server.MapPath(
    "./images/worldmap4.gif"));
Bitmap imgBitmap = new Bitmap(image1);

Now we make a loop through the 2 dimensions of the image, map phi and theta angles from image coordinates, get the cartesian 3D coordinates from phi and theta, provide some rotation to the obtained 3D points and plot them with respective image color:

for (int i = 0; i < imgBitmap.Width; i++)
     {
     for (int j = 0; j < imgBitmap.Height; j++)
          {
          // map the angles from image coordinates
          double theta = Algebra.MapCoordinate(0.0, imgBitmap.Width - 1,
              theta1, theta0, i);
          double phi = Algebra.MapCoordinate( 0.0, imgBitmap.Height - 1,phi0,
              phi1, j);
          // find the cartesian coordinates
          double x = radius * Math.Sin(phi) * Math.Cos(theta);
          double y = radius * Math.Sin(phi) * Math.Sin(theta);
          double z = radius * Math.Cos(phi);
          // apply rotation around X and Y axis to reposition the sphere
          RotX(1.5, ref y, ref z);
          RotY(-2.5, ref x, ref z);
          // plot only positive points
          if (z > 0)
               {
               Color color = imgBitmap.GetPixel(i, j);
               Brush brs = new SolidBrush(color);
               int ix = (int)x + 100;
               int iy = (int)y + 100;
               graphics.FillRectangle(brs, ix, iy, 1, 1);
               brs.Dispose();
              }
          }
     }

The Rotation Functions [almost forgot]

Actually I made a 3D Math class, but here you will need only these functions

public static void RotX(double angle, ref double y, ref double z)
     {
     double y1 = y * System.Math.Cos(angle) - z * System.Math.Sin(angle);
     double z1 = y * System.Math.Sin(angle) + z * System.Math.Cos(angle);
     y = y1;
     z = z1;
     }
public static void RotY(double angle, ref double x, ref double z)
     {
     double x1 = x * System.Math.Cos(angle) - z * System.Math.Sin(angle);
     double z1 = x * System.Math.Sin(angle) + z * System.Math.Cos(angle);
     x = x1;
     z = z1;
     }
public static void RotZ(double angle, ref double x, ref double y)
     {
     double x1 = x * System.Math.Cos(angle) - y * System.Math.Sin(angle);
     double y1 = x * System.Math.Sin(angle) + y * System.Math.Cos(angle);
     x = x1;
     y = y1;
     }

See sample

License

This article, along with any associated source code and files, is licensed under The GNU General Public License (GPLv3)

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About the Author

andalmeida
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Comments and Discussions

 
QuestionCan not find the complete ource code Pinmembermans.098724-Jan-13 5:02 
GeneralMy vote of 5 Pinmembermanoj kumar choubey26-Feb-12 21:44 
QuestionAny ideas to make it faster? PinmemberTiramisung1-Apr-10 16:16 
AnswerRe: Any ideas to make it faster? Pinmemberandalmeida2-Apr-10 3:55 
GeneralRe: Any ideas to make it faster? PinmemberTiramisung4-Apr-10 22:07 
GeneralI really upset! PinmemberMr. Cencious12-Nov-07 23:28 
GeneralRe: I really upset! Pinmemberandalmeida13-Nov-07 0:56 
GeneralRe: I really upset! PinmemberMr. Cencious15-Nov-07 16:15 
GeneralRe: I really upset! PinmemberMr. Cencious29-Nov-07 20:41 
GeneralRotation Pinmemberseeblunt11-Aug-07 17:36 
GeneralRe: Rotation Pinmemberseeblunt11-Aug-07 18:02 
GeneralRe: Rotation Pinmemberandalmeida12-Aug-07 14:04 
QuestionMapping an image Cylindrical Surface Pinmemberzhongyisun10-Aug-07 6:27 
AnswerRe: Mapping an image Cylindrical Surface Pinmemberandalmeida10-Aug-07 7:24 
GeneralRe: Mapping an image Cylindrical Surface Pinmemberzhongyisun10-Aug-07 7:45 
GeneralCurve tracing algorithm PinmemberGD602-Aug-07 12:09 
GeneralRe: Curve tracing algorithm Pinmemberandalmeida3-Aug-07 2:50 
GeneralRe: Curve tracing algorithm PinmemberGD605-Aug-07 11:03 
QuestionWhy? PinmemberPaul Selormey23-Jul-07 20:41 
AnswerRe: Why? Pinmemberandalmeida24-Jul-07 2:39 
AnswerRe: Why? Pinmemberandalmeida25-Jul-07 5:57 
AnswerRe: Why? PinmemberPaul Selormey25-Jul-07 6:24 
AnswerRe: Why? PinmemberJohnno7430-Jul-07 13:39 
AnswerRe: Why? PinmemberPatrick Sears31-Jul-07 9:55 
GeneralRe: Why? Pinmemberandalmeida31-Jul-07 9:58 
GeneralRe: Why? PinmemberPatrick Sears31-Jul-07 10:17 
GeneralRe: Why? PinmemberWerdna13-Aug-07 4:57 
Jokesweet PinmemberBen Daniel23-Jul-07 18:10 
AnswerRe: sweet Pinmemberandalmeida24-Jul-07 3:53 
GeneralRe: sweet PinmemberN.L. Neilson2-Aug-07 11:01 
GeneralRe: sweet Pinmemberandalmeida2-Aug-07 11:03 
GeneralRe: sweet Pinmemberandalmeida2-Aug-07 11:17 
GeneralRe: sweet PinmemberN.L. Neilson2-Aug-07 11:51 
GeneralRe: sweet Pinmemberandalmeida2-Aug-07 11:51 
GeneralRe: sweet PinmemberN.L. Neilson2-Aug-07 13:48 

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