Any point on a sphere
Author
Hi,
could somone point me in the right direction to calculating any point on a sphere, given the radius of the sphere. Im wanting to "plot" a sphere by looping through each point on the sphere.
Regards
Asheh
Do you mean: random point on a sphere?
Or do you want to generate a sequence of points of a sphere in some uniform manner?
Or do you want to generate a sequence of points of a sphere in some uniform manner?
P=C+D*r where P is a point on the sphere, D is a random direction (normalized), r is the radius of the sphere and C is the center of your sphere.
Quote:could somone point me in the right direction to calculating any point on a sphere, given the radius of the sphere.Im wanting to "plot" a sphere by looping through each point on the sphere.
Some clarity please, a sphere has <insert very very large number here> of points which lie on its surface. It sounds like you are asking how to find all the points and then plot them.
A point lies on the surface of a sphere if the magnitude of the vector between the point and the center of the sphere is equal to the spheres radius.
Author
Quote:Original post by deffer
Do you mean: random point on a sphere?
Or do you want to generate a sequence of points of a sphere in some uniform manner?
the latter, yes
Quote:Original post by AshehQuote:Original post by deffer
Do you mean: random point on a sphere?
Or do you want to generate a sequence of points of a sphere in some uniform manner?
the latter, yes
As I can see, you don't seek for plotting points, but to build a sphere from triangles. From then, you can plot only points of the triangles, or draw full-blown sphere.
A search for "sphere triangulation" gives this thread, for example.
Author
hmm not really, im plotting a set of objects, in the shape of a sphere, they arent to be joined
Let's first look at approximating a circle with some points: (In C++, though you could probably figure out any other language from this)
Okay, that's pretty simple. It just loops through MAX_POINTS number of angles in a circle and plots point RADIUS away from the origin.
Now, for a sphere, we'll start with the same code as before. However, now we have to make a new circle every loop instead of a circle. We'll achieve this with two nested loops:
Notice how the first loop only loops to PI, not to 2 PI. This is because a circle also covers the part of the circle opposite from the first point, hence we only have to go half-way around. Also, I haven't tested this, and actually just 'guessed' the last half.
Hope that helps (and works)!
[Edit: changed ints to floats.]
for(int i = 0; i < MAX_POINTS; i++){ float angle = i/MAX_POINTS * 2 * PI; //Calculates the point's position float x = cos(angle)*RADIUS; float y = sin(angle)*RADIUS; AddPoint(x,y);//Adds the point to your list, or plots it, or does whatever you want to do with the point}Okay, that's pretty simple. It just loops through MAX_POINTS number of angles in a circle and plots point RADIUS away from the origin.
Now, for a sphere, we'll start with the same code as before. However, now we have to make a new circle every loop instead of a circle. We'll achieve this with two nested loops:
for(int i = 0; i < MAX_POINTS; i++){ //The angle around the equator: float xAngle = i/MAX_POINTS * PI;//Note: No longer multiply by 2 //Now create a circle that intersects for(int j = 0; j < MAX_POINTS; j++) { float zAngle = j/MAX_POINTS * 2 * PI; //Calculates the point's position float x = cos(xAngle)*RADIUS*cos(yAngle); float y = sin(xAngle)*RADIUS*cos(yAngle); float z = cos(xAngle)*RADIUS*sin(yAngle); AddPoint(x,y,z); }}Notice how the first loop only loops to PI, not to 2 PI. This is because a circle also covers the part of the circle opposite from the first point, hence we only have to go half-way around. Also, I haven't tested this, and actually just 'guessed' the last half.
Hope that helps (and works)!
[Edit: changed ints to floats.]
Quote://Calculates the point's position
float x = cos(xAngle)*RADIUS*cos(yAngle);
float y = sin(xAngle)*RADIUS*cos(yAngle);
float z = cos(xAngle)*RADIUS*sin(yAngle);
That should read:
float z = RADIUS*sin(yAngle);
note that the method suggest is NOT uniform. You need to find any (rectangular) equal area projection of the sphere and generate coordinates on the map.
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