Spherical Coordinates in C#

Example5_7

Introduction

Normally, the Cartesian coordinate system is used in transformations and projections for graphics objects. In this case, you simply specify a point using XY, and coordinates. In practice, other coordinate systems can also be applied, and are sometimes more convenient than the Cartesian coordinate system.
In this article, I will discuss the spherical coordinate system in 3D space and show you how to create the spherical graphics objects in this system.

Background

In the spherical coordinate system, a point is specified by r, θ, and φ. Here r is the distance from the point to the origin, θ is the polar angle, and φ is the azimuthal angle in the XZ plane from the axis. In this notation, I alternate the conventional and axes so that the computer screen is described by the Xplane. Figure 1 shows a point in this spherical coordinate system

Figure 1: Spherical coordinate system.
From this figure, we can obtain the following relationships:

The spherical coordinates (r, θ, φ) are related to the Cartesian coordinates by:

Sometimes it is more convenient to create sphere-like objects in terms of the spherical coordinate system. The following example application program will create two spheres. We need to add the Matrix3 and Point3classes to the current project. And also add a new class, DrawSphere, to the project.
Now we need to add a Spherical method to the Matrix3 class. The Matrix3 class has been discussed in Chapter 5 of my new book “Practical C# Charts and Graphics“.

public Point3 Spherical(float r, float theta, float phi)
{
    Point3 pt = new Point3();
    float snt = (float)Math.Sin(theta * Math.PI / 180);
    float cnt = (float)Math.Cos(theta * Math.PI / 180);
    float snp = (float)Math.Sin(phi * Math.PI / 180);
    float cnp = (float)Math.Cos(phi * Math.PI / 180);
    pt.X = r * snt * cnp;
    pt.Y = r * cnt;
    pt.Z = -r * snt * snp;
    pt.W = 1;
    return pt;
}

This method transforms a point in the spherical coordinate system to a point in the Cartesian coordinate system. We then Add a DrawSphere class to the project. This class allows you to specify the radius and positions (the center location) of a sphere object. The SphereCoordinates method in this class creates the points on a sphere surface by specifying their longitude and latitude. The DrawIsometricView draws the sphere using the isometric projection.

Using the code

This application can be tested using the following Form1 class:

using System;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Windows.Forms;
namespace Example5_6
{
    public partial class Form1 : Form
    {
      public Form1()
      {
            InitializeComponent();
            this.SetStyle(ControlStyles.ResizeRedraw, true);
            // Subscribing to a paint eventhandler to drawingPanel:
            panel1.Paint += new PaintEventHandler(panel1Paint);
      }
      private void panel1Paint(object sender, PaintEventArgs e)
      {
            Graphics g = e.Graphics;
            g.SmoothingMode = SmoothingMode.AntiAlias;
            float a = panel1.Height / 3;
            DrawSphere ds = new DrawSphere(this, a, 0, 0, -a / 2);
            ds.DrawIsometricView(g);
            ds = new DrawSphere(this, 2 * a / 3, -a/2, -a/2, a / 2);
            ds.DrawIsometricView(g);
      }
    }
}

Here we create two spheres with different radii and positions. By building and running this project, you should obtain the results shown in Figure 2.

Figure 2: Spheres created in a spherical coordinate system.
This project is from the examples (example5-6 in Chapter 5) of the new book “Practical C# Charts and Graphics”, where you can find more advanced chart and graphics programming for real-world .NET applications. For more information, please visit the website at www.publishing.unicadinc.com

About the Author

Dr. Jack Xu has a Ph.D in theoretical physics. He has over 15 years programming experience in Basic, Fortran, C, C++, Matlab, and C#, specializing in numerical computation methods, algorithms, physical modeling, computer-aided design (CAD) development, graphics user interface, and 3D graphics. Currently, he is responsible for developing commercial CAD tools based on Microsoft .NET framework.
Please read my other articles:

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  135. I’m amazed, I must say. Rarely do I come across a blog that’s equally educative and interesting, and let me tell you, you’ve hit the nail on the head. The problem is something which not enough men and women are speaking intelligently about. Now i’m very happy I came across this in my search for something relating to this.

  136. An outstanding share! I have just forwarded this onto a colleague who has been doing a little homework on this. And he actually ordered me lunch because I discovered it for him… lol. So allow me to reword this…. Thank YOU for the meal!! But yeah, thanx for spending some time to talk about this matter here on your internet site.

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  158. Having read this I believed it was very informative. I appreciate you finding the time and effort to put this informative article together. I once again find myself personally spending a lot of time both reading and commenting. But so what, it was still worth it!

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  169. An impressive share! I have just forwarded this onto a co-worker who had been doing a little research on this. And he actually bought me breakfast simply because I discovered it for him… lol. So allow me to reword this…. Thank YOU for the meal!! But yeah, thanx for spending time to talk about this issue here on your internet site.

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  172. Next time I read a blog, Hopefully it does not fail me as much as this one. I mean, Yes, it was my choice to read through, but I actually believed you would have something useful to say. All I hear is a bunch of crying about something you could fix if you weren’t too busy seeking attention.

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  177. Hi, I do believe this is an excellent website. I stumbledupon it 😉 I am going to come back yet again since I saved as a favorite it. Money and freedom is the greatest way to change, may you be rich and continue to guide others.

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  182. Good post. I learn something new and challenging on sites I stumbleupon on a daily basis. It’s always interesting to read content from other writers and practice something from other websites.

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  184. May I simply say what a relief to uncover a person that really knows what they are discussing over the internet. You certainly understand how to bring an issue to light and make it important. More people really need to look at this and understand this side of your story. It’s surprising you aren’t more popular because you certainly possess the gift.

  185. Howdy! I could have sworn I’ve been to this blog before but after going through a few of the posts I realized it’s new to me. Regardless, I’m definitely happy I came across it and I’ll be bookmarking it and checking back often!

  186. Having read this I thought it was really informative. I appreciate you finding the time and energy to put this short article together. I once again find myself spending a significant amount of time both reading and leaving comments. But so what, it was still worthwhile!

  187. You are so awesome! I don’t suppose I have read through something like this before. So good to find another person with some original thoughts on this topic. Seriously.. many thanks for starting this up. This website is one thing that is required on the web, someone with a little originality!

  188. Hello there, I do think your blog could possibly be having web browser compatibility issues. When I take a look at your web site in Safari, it looks fine however, when opening in IE, it has some overlapping issues. I just wanted to give you a quick heads up! Aside from that, excellent blog!

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  190. Can I simply just say what a relief to discover somebody who actually understands what they are talking about on the web. You certainly know how to bring a problem to light and make it important. More people should check this out and understand this side of your story. I was surprised you aren’t more popular given that you certainly have the gift.

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  194. Can I simply just say what a relief to find somebody that really knows what they are talking about online. You actually realize how to bring a problem to light and make it important. More people have to look at this and understand this side of the story. I can’t believe you aren’t more popular since you most certainly have the gift.

  195. I would like to thank you for the efforts you’ve put in penning this blog. I really hope to check out the same high-grade content by you later on as well. In truth, your creative writing abilities has motivated me to get my own website now 😉

  196. Having read this I believed it was very enlightening. I appreciate you spending some time and effort to put this article together. I once again find myself personally spending a significant amount of time both reading and leaving comments. But so what, it was still worth it!

  197. Hi, I do think this is a great site. I stumbledupon it 😉 I’m going to come back once again since i have bookmarked it. Money and freedom is the best way to change, may you be rich and continue to guide other people.

  198. You are so awesome! I don’t think I have read anything like that before. So wonderful to discover someone with unique thoughts on this topic. Really.. many thanks for starting this up. This website is one thing that is required on the internet, someone with a little originality!

  199. Aw, this was a really nice post. Taking a few minutes and actual effort to create a good article… but what can I say… I put things off a lot and don’t seem to get nearly anything done.

  200. Oh my goodness! Amazing article dude! Many thanks, However I am having difficulties with your RSS. I don’t know the reason why I can’t subscribe to it. Is there anyone else having similar RSS issues? Anybody who knows the answer will you kindly respond? Thanx!!

  201. Can I simply say what a relief to discover an individual who truly understands what they’re talking about online. You certainly realize how to bring an issue to light and make it important. More people must check this out and understand this side of the story. I was surprised that you aren’t more popular because you most certainly have the gift.

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  203. Having read this I thought it was very informative. I appreciate you finding the time and effort to put this informative article together. I once again find myself personally spending way too much time both reading and posting comments. But so what, it was still worthwhile!

  204. A fascinating discussion is worth comment. I do think that you should write more about this topic, it might not be a taboo subject but usually people don’t speak about these subjects. To the next! Best wishes!!

  205. An outstanding share! I’ve just forwarded this onto a colleague who has been doing a little homework on this. And he actually bought me lunch because I stumbled upon it for him… lol. So let me reword this…. Thanks for the meal!! But yeah, thanks for spending time to talk about this issue here on your internet site.

  206. An outstanding share! I’ve just forwarded this onto a coworker who has been conducting a little research on this. And he in fact bought me breakfast simply because I stumbled upon it for him… lol. So let me reword this…. Thank YOU for the meal!! But yeah, thanx for spending time to talk about this issue here on your blog.

  207. You’re so awesome! I don’t suppose I have read something like this before. So wonderful to discover someone with unique thoughts on this issue. Seriously.. many thanks for starting this up. This web site is one thing that is needed on the web, someone with some originality!

  208. After I initially left a comment I seem to have clicked on the -Notify me when new comments are added- checkbox and now whenever a comment is added I recieve four emails with the same comment. Perhaps there is a means you can remove me from that service? Kudos!

  209. You’ve made some really good points there. I looked on the internet to find out more about the issue and found most individuals will go along with your views on this website.

  210. Good post. I learn something totally new and challenging on sites I stumbleupon everyday. It will always be helpful to read content from other writers and use something from their websites.

  211. Oh my goodness! Amazing article dude! Many thanks, However I am having difficulties with your RSS. I don’t understand why I can’t join it. Is there anybody else getting similar RSS issues? Anyone who knows the answer will you kindly respond? Thanks!!

  212. Oh my goodness! Amazing article dude! Thank you, However I am encountering difficulties with your RSS. I don’t understand the reason why I cannot subscribe to it. Is there anybody having identical RSS issues? Anybody who knows the solution will you kindly respond? Thanx!!

  213. Hi, I do believe this is an excellent blog. I stumbledupon it 😉 I’m going to come back once again since i have saved as a favorite it. Money and freedom is the greatest way to change, may you be rich and continue to guide other people.

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  216. Greetings, I do believe your web site may be having web browser compatibility issues. Whenever I look at your web site in Safari, it looks fine however, if opening in I.E., it’s got some overlapping issues. I just wanted to provide you with a quick heads up! Apart from that, excellent site!

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  218. Howdy! This blog post couldn’t be written much better! Looking at this post reminds me of my previous roommate! He constantly kept preaching about this. I most certainly will send this information to him. Pretty sure he’ll have a good read. Thanks for sharing!

  219. You’re so interesting! I don’t suppose I’ve read through a single thing like that before. So nice to find somebody with unique thoughts on this issue. Seriously.. thank you for starting this up. This website is one thing that’s needed on the web, someone with a little originality!

  220. Your style is very unique compared to other folks I’ve read stuff from. I appreciate you for posting when you’ve got the opportunity, Guess I’ll just book mark this site.

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  222. Hello there! I could have sworn I’ve been to this site before but after looking at many of the posts I realized it’s new to me. Anyhow, I’m certainly pleased I found it and I’ll be bookmarking it and checking back regularly!

  223. An outstanding share! I have just forwarded this onto a friend who has been conducting a little homework on this. And he actually ordered me dinner simply because I stumbled upon it for him… lol. So let me reword this…. Thanks for the meal!! But yeah, thanx for spending the time to discuss this issue here on your website.

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  226. The very next time I read a blog, Hopefully it won’t fail me as much as this one. After all, Yes, it was my choice to read, however I really believed you’d have something useful to say. All I hear is a bunch of complaining about something that you can fix if you weren’t too busy seeking attention.

  227. I have to thank you for the efforts you have put in writing this website. I really hope to check out the same high-grade blog posts by you in the future as well. In fact, your creative writing abilities has motivated me to get my own, personal site now 😉

  228. I must thank you for the efforts you’ve put in writing this website. I’m hoping to see the same high-grade content from you in the future as well. In truth, your creative writing abilities has motivated me to get my own, personal blog now 😉

  229. The next time I read a blog, I hope that it does not disappoint me just as much as this one. After all, I know it was my choice to read through, but I actually believed you’d have something helpful to talk about. All I hear is a bunch of complaining about something you can fix if you weren’t too busy searching for attention.

  230. Hi! I could have sworn I’ve visited this site before but after going through some of the posts I realized it’s new to me. Anyways, I’m definitely delighted I came across it and I’ll be bookmarking it and checking back regularly!

  231. Hi, I do think this is an excellent blog. I stumbledupon it 😉 I am going to return yet again since I book marked it. Money and freedom is the greatest way to change, may you be rich and continue to help other people.

  232. You are so awesome! I do not think I have read through a single thing like this before. So great to find someone with unique thoughts on this issue. Really.. many thanks for starting this up. This site is something that is required on the web, someone with some originality!

  233. Having read this I thought it was very informative. I appreciate you finding the time and energy to put this informative article together. I once again find myself spending a lot of time both reading and commenting. But so what, it was still worthwhile!

  234. You’re so cool! I do not believe I’ve truly read anything like this before. So nice to find another person with a few unique thoughts on this subject matter. Really.. thank you for starting this up. This web site is one thing that is required on the internet, someone with a little originality!

  235. Hello there, I think your website might be having internet browser compatibility problems. When I take a look at your website in Safari, it looks fine however, when opening in Internet Explorer, it’s got some overlapping issues. I just wanted to give you a quick heads up! Other than that, great site!

  236. An interesting discussion is definitely worth comment. I think that you need to publish more about this topic, it may not be a taboo matter but generally people don’t discuss these issues. To the next! Many thanks!!

  237. Your style is really unique compared to other folks I’ve read stuff from. Thank you for posting when you have the opportunity, Guess I will just book mark this blog.

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