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codeslasher

Post subject: Polygons for a sphere shape Posted: Wed Nov 28, 2007 10:20 am 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Hi guys and gals,
I'd like to ask if anyone knows of a good way to generate the polygons for a sphere generated from code?
I want to have a sphere shape as a primitive and use the equation for a sphere to generate the vertices for the sphere. However, I don't know how to group vertices to make up the triangles/quads for a poly on the shpere.
Basically want to do something similar to Marek's cube/cylinder classes.
Thanks,
Codeslasher
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Marek

Post subject: Re: Polygons for a sphere shape Posted: Wed Nov 28, 2007 9:57 pm 
Joined: Sun Feb 11, 2007 8:59 am Posts: 1102 Location: Ontario Canada

The was that I have done this in the past is like this:
two nested for loops. one going from +90 to 90 degrees and the other going from 0 to 180 degrees. These two angles define where each point will sit on the sphere. the top and bottom of the sphere is created with triangles that connect at the top and bottom points of the sphere (+/90). All other segments are joined together similar to how the flat grid works.
Last edited by Marek on Mon Jan 07, 2008 9:03 pm, edited 1 time in total.





codeslasher

Post subject: Re: Polygons for a sphere shape Posted: Sat Dec 01, 2007 6:29 pm 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Hi Marek,
I use the following code to generate the points on the sphere:
(I want to be able to control the increment for the angles so I specify phiInc and alphaInc as
phiInc = 360 / number_steps
alphaInc = 180 / number_steps
for(int phi = 180; phi <= 180; phi += phiInc)
{
phiRadian = (phi * PI) / 180.0;
for(int alpha = 90; alpha <= 90; alpha += alphaInc)
{
alphaRadian = (alpha * PI) / 180.0;
x = RADIUS*sin(phiRadian)*cos(alphaRadian);
y = RADIUS*sin(phiRadian)*sin(alphaRadian);
z = RADIUS*cos(phiRadian);
glBegin(GL_POINTS);
glVertex3f(x,y,z);
glEnd();
}
}
However, I seem to be getting double the number of points I want.
For instance, If I want sphere to be divided into steps of 5 points, I get 10 points.
Does my code look correct?
Thanks





codeslasher

Post subject: Re: Polygons for a sphere shape Posted: Sat Dec 01, 2007 8:30 pm 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Also the sphere seems a little "squashed".
Also I've changed the equations (swapped their places) so that
Y = RADIUS * cos (phiRadian)
and
Z = RADIUS * sin (phiRadians) * sin (alphaRadians)
I did this because the poles were not at the top and bottom but at the sides using the code in the previous post.





Marek

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 7:12 am 
Joined: Sun Feb 11, 2007 8:59 am Posts: 1102 Location: Ontario Canada

I quickly sketched your setup and I think these are the coordinates that you should be using:
x = RADIUS * sin(alphaRadians) * cos (phiRadians);
y = RADIUS * cos(alphaRadians);
z = RADIUS * sin(alphaRadians) * sin (phiRadians);
Last edited by Marek on Mon Jan 07, 2008 9:05 pm, edited 1 time in total.





codeslasher

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 8:45 am 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Hi,
(Your equations work. But I want to understand why mine didn't)
I used the image at this link
http://upload.wikimedia.org/wikipedia/c ... re.svg.png
and books to come up with my equations.
However, they do not match exactly. To be able to go from 90 to 90 on Phi and 180 to 180 on alpha, I had to use these equations
for(int phi = 90; phi <= 90; phi += phiInc)
{
phiRadian = (phi * PI) / 180.0;
y = RADIUS*sin(phiRadian);
for(int alpha = 180; alpha <= 180; alpha += alphaInc)
{
alphaRadian = (alpha * PI) / 180.0;
x = RADIUS*cos(phiRadian)*sin(alphaRadian);
z = RADIUS*cos(phiRadian)*cos(alphaRadian);
}
}
Why couldn't I code it straight as it was in the image and math books?
Thanks.





Marek

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 9:54 am 
Joined: Sun Feb 11, 2007 8:59 am Posts: 1102 Location: Ontario Canada

The difference between the equations that I gave you and the ones that you were using was the coordinate system.
Knowing that OpenGL has X to the right, Y up and Z in/out of the screen. You had said you want your poles to be at the top/bottom of the sphere.
Since alpha goes from 90 to +90 that tells me you want alpha to sweep from the south to the north pole.
Phi goes from 180 to +180 which says this is going to represent your latitude lines on the sphere.
I drew a sketch to show how everything is setup. http://www.marekknows.com/Misc/forum/Sphere.jpg
The dashed lines are the values you need to calculate for each point on the sphere.
The green dashed line on the XY plane is equal to RADIUS * sin(alphaRadians)
The blue and black ones arethe X and Z coordinates respectively. The red one is the Y coordinate
Last edited by Marek on Mon Jan 07, 2008 9:06 pm, edited 1 time in total.





codeslasher

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 11:47 am 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Thanks for the nice explanation.





codeslasher

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 3:14 pm 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

I've attached the c code which uses glut and opengl.
I decided to use Marek's equations just to see what happens.
I can't seem to get any of the equations to give me the points I expect.
for example, I don't get 2 poles.
Using Marek's last set of equations I get a hemisphere.
If its not too much to ask, can you look at this and change it so I see what am doing wrong.
http://www.freewebs.com/fuzionstudio/sphere.cpp
Thanks





Marek

Post subject: Re: Polygons for a sphere shape Posted: Sun Dec 02, 2007 5:03 pm 
Joined: Sun Feb 11, 2007 8:59 am Posts: 1102 Location: Ontario Canada

I took a look at your code and fixed it. Here is the updated version. http://www.marekknows.com/Misc/forum/sphere.cpp
When working with sin/cos in c++ you have to be careful with the values that you are going to get. To handle these special cases, notice that I added a few (?:) statements to make sure the sign of the result is correct. You also have to handle the special case where alpha=0 separately as shown.
You will notice that under certain cases when the number of sections is larger than 6, the lower and upper hemisphere do not line up. longitude lines don't meet at the equator. This is because the values returned from the cos/sin function are different for +ve and ve numbers. I would say calculate all the points for the top hemisphere (excluding the equator) and then mirror these points for the bottom half just by swapping the y value to be ve rather than calculating them. This way you will always have the same spacing for all the points in the top and bottom half.
Handle the equator separately.
Last edited by Marek on Mon Jan 07, 2008 9:07 pm, edited 1 time in total.





codeslasher

Post subject: Posted: Sat Dec 08, 2007 8:56 am 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Just a little update,
Have gottent the sphere to render itself.
A video can be found at
http://www.youtube.com/watch?v=rbLTxz8vo
next thing am working on is lighting and normals, then textures.
Keep you posted.





codeslasher

Post subject: Posted: Sat Dec 08, 2007 9:42 pm 
Joined: Sat Jun 23, 2007 7:56 pm Posts: 145

Hi people,
now have normals and shading on the sphere.
I used the the actual points on the sphere as the normals. (Tried many approaches before deciding to use the points generated along the sphere as the normals)
You can see the results below
http://www.youtube.com/watch?v=UJbmim_l4o
It is not 100% accurate, for example, if light strikes it from certain angles e.g straight from above, the shading is off.
Working on improving this. Also, I enabled GL_NORMALIZE to aid in keeping the normals accurate.
Marek, I tried generating normals using the plane equations with 3 points on a triangle, the results weren't great. Am I right to assume that the points along the sphere suffice as normals?





Marek

Post subject: Posted: Mon Jan 07, 2008 9:02 pm 
Joined: Sun Feb 11, 2007 8:59 am Posts: 1102 Location: Ontario Canada

codeslasher wrote: Marek, I tried generating normals using the plane equations with 3 points on a triangle, the results weren't great. Am I right to assume that the points along the sphere suffice as normals?
Nice video's on youTube! Great work.
I've decided to add a new geometry Sphere object to the physics engine so you'll be able to compare how I implement the same thing to your code. Check out VMK2 in the physics engine.
The normal at each vertex should point away from the sphere's surface. However if you extend the normal line inward, into the sphere, it should pass right through the centre of the sphere.











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