This example shows how you can draw spheres in a 3D WPF program. The following code shows the `AddSphere` method, which adds a sphere to a `MeshGeometry3D`. It’s kind of long, but the ideas (which I’ll explain shortly) aren’t too complicated.

// Add a sphere. private void AddSphere(MeshGeometry3D mesh, Point3D center, double radius, int num_phi, int num_theta) { double phi0, theta0; double dphi = Math.PI / num_phi; double dtheta = 2 * Math.PI / num_theta; phi0 = 0; double y0 = radius * Math.Cos(phi0); double r0 = radius * Math.Sin(phi0); for (int i = 0; i < num_phi; i++) { double phi1 = phi0 + dphi; double y1 = radius * Math.Cos(phi1); double r1 = radius * Math.Sin(phi1); // Point ptAB has phi value A and theta value B. // For example, pt01 has phi = phi0 and theta = theta1. // Find the points with theta = theta0. theta0 = 0; Point3D pt00 = new Point3D( center.X + r0 * Math.Cos(theta0), center.Y + y0, center.Z + r0 * Math.Sin(theta0)); Point3D pt10 = new Point3D( center.X + r1 * Math.Cos(theta0), center.Y + y1, center.Z + r1 * Math.Sin(theta0)); for (int j = 0; j < num_theta; j++) { // Find the points with theta = theta1. double theta1 = theta0 + dtheta; Point3D pt01 = new Point3D( center.X + r0 * Math.Cos(theta1), center.Y + y0, center.Z + r0 * Math.Sin(theta1)); Point3D pt11 = new Point3D( center.X + r1 * Math.Cos(theta1), center.Y + y1, center.Z + r1 * Math.Sin(theta1)); // Create the triangles. AddTriangle(mesh, pt00, pt11, pt10); AddTriangle(mesh, pt00, pt01, pt11); // Move to the next value of theta. theta0 = theta1; pt00 = pt01; pt10 = pt11; } // Move to the next value of phi. phi0 = phi1; y0 = y1; r0 = r1; } }

This method basically loops variable `phi` through values between 0 and π. The value `phi` represents an angle of rotation down from the vertical Y axis as shown in the figure on the right.

For each value of `phi`, the method loops variable `theta` through the values between 0 and 2 * π. The value `theta` represents a rotation around the Y axis as shown in the figure on the right.

Together `phi` and `theta` determine the spherical coordinates of a point. (If you’re familiar with spherical coordinates, you can skip the next two paragraphs.)

Consider the blue triangle shown in the picture. This is a right triangle (the radius is the hypotenuse), so the length of the side along the Y axis is `y0 = radius * cos(phi)` and the length of the side parallel to the X-Z plane has length `r0 = radius * sin(phi)`.

Now consider the green triangle shown in the picture. It’s a right triangle with the dashed line as its hypotenuse. Its hypotenuse has the same length (and is parallel to) the line labeled r0. In that case the point’s X coordinate is given by `x0 = r0 * cos(theta)` and `z0 = r0 * sin(theta)`.

That’s how the program uses spherical coordinates to calculate the Cartesian coordinates of the points on the sphere. The picture on the right shows the points calculated for particular values of `phi` and `theta`.

Having found those points, the code simply calls the `AddTriangle` method to create the triangles `pt00-pt11-pt10` and `pt00-pt01-pt11`.

The rest of the program is similar to previous examples that make 3D drawings in WPF. Download the example to see the details.

Hello Rod,

Quick question, what application and techniques do you use for creating the illustrations on your blog posts? Will be helpful.

Thank you.

They are mostly just screen shots of Visual Studio programs. Occasionally I make a drawing in a Word document and take a screen shot of that.