Clever Geek Handbook

Sphere Click

I have a unit sphere (radius 1) that is centered on an orthographic projection.

The sphere can rotate freely.

How to determine the point on the sphere that the user clicks on?

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2 answers


Given:

  • monitor height and width
  • radius of the projected circle, in pixels
  • coordinates of the point the user clicked on

And assuming the top left corner is (0,0), the x value increases as you move to the right, and the y value increases as you move down.

Move the user's click point to the coordinate space of the globe.

userPoint.x -= monitor.width/2
userPoint.y -= monitor.height/2
userPoint.x /= circleRadius
userPoint.y /= circleRadius

Find the z coordinate of the intersection point.



//solve for z
//x^2 + y^2 + z^2 = 1
//we know x and y, from userPoint
//z^2 = 1 - x^2 - y^2
x = userPoint.x
y = userPoint.y

if (x^2 + y^2 > 1){
    //user clicked outside of sphere. flip out
    return -1;
}

//The negative sqrt is closer to the screen than the positive one, so we prefer that.
z = -sqrt(1 - x^2 - y^2);

Now that you know the intersection point (x, y, z), you can find the latitude and longitude.

Assuming the center of the globe facing the user is 0E 0N,

longitude = 90 + toDegrees(atan2(z, x));
lattitude = toDegrees(atan2(y, sqrt(x^2 + z^2)))

If the ball spins so that the 0E meridian is not facing directly towards the viewer, subtract the angle of rotation from the longitude.

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One possible approach is to create a sphere of triangles with rows and columns. They can also be invisible. And then hit testing these triangles with the mouse rays.

Latitude / longitude grid



Check out this latitude / longitude grid, but apply a lot more tightly. For each grid cell, you need two triangles.

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