# Correctness or otherwise of the procedure for generating an orbiting camera in WebGl

I have to create a orbiting camera. I created the model of sun (a sphere) around (0,0,0) , triangulated and Phong shaded it. I would have a camera that goes around the sun thus an orbiting camera and I would know if my way to proceed is right or not: In WebGl there isn't a phisical camera. Nevertheless I imagine to place my camera at the center (0,0,0) and I have first to translate it of [0 0 100] ([0 0 100] is the point where early is located the camera) and later I rotate the camera around y ([0 1 0]) of some angle (Actually the angle is animated, i.e. the angle increases over time).

Thus cameraMatrix = R(angle,[0 1 0])T([0 0 100]) (First translation and later rotation)

But in WebGl there isn't camera, then I have to move the world with inverse transformation namely:

ModelViewMatrix = inverse(cameraMatrix);

Thus ModelViewMatrix = inverse{R(angle,[0 1 0])T([0 0 100])} = inverse(T([0 0 100]))inverse(R(angle,[0 1 0])= T([0 0 -100]) R(-angle,[0 1 0])

(In the last first rotation and later translation)

So far is it all right? Finally in drawScene namely the function of rendering cycle the order of call is inverted namely:

mat4.translate(mvMatrix , [0,0,-100.0]);


in this order does a rototranslation, namely it occurs first the rotation and later the translation (inverted respect the order of call functions).

I would confirm if this is right because I'm a neophyte of Computer Graphics and I'm not sure. (I know that I can use lookAt() or define the values of cameraMatrix by hand but I'm not interested in it). Thanks in advance

Your math looks correct to me. Your terminology is a little off - technically what you are creating here is just the 'view' matrix rather than the 'modelView'. If you're just drawing a single sphere at the origin then it doesn't make a difference, but normally the modelView is unique for each object in a scene - it's the object's model-to-world transform matrix multiplied by the view matrix you describe above.

• There are early 2 spheres centered at the origin. Then the MVmatrix is different for the 2 objects namely I draw a sphere with a translate value and another sphere with another translation value thus in the same rendering cycle I modify the MVmatrix. Isn't this correct? Actually I would realize that a sphere, the Earth, goes around another sphere the Sun but I have some difficult for this rason I want know if my math was mistakes less. – Umbert Jun 17 '18 at 7:58
• Normally you have a 'transform' - rotation scale and translation - for each object in the world. You can calculate a separate 'model' matrix for each object from these that places it correctly in the world. Then you calculate a single 'view' matrix for the camera, which is the inverse of its transform like you describe above. To then get a single object's position relative to the camera, you multiply view*model to get the modelView for that object. – russ Jun 17 '18 at 13:16
• Yes, you are right in general. But in my case is a little more complicated because in the meantime I have to rotate the Earth around the sun. However, assured that my way of generating an orbiting camera is correct I will open a more specific topic. Thanks! – Umbert Jun 17 '18 at 15:01