Moving about in space

• Our Demo for the day.
• We would like to move the camera in space.
• Remember the camera has three properties
  • A current location, specified in modeling coordinates
  • A Look At point, specified in modeling coordinates
  • An up vector.
• In the new code.

  • NewView( camera, at, up) {
        var eye = lookAt(camera, at, up);
        var proj =  this.Frustum(-1, 1, -1, 1, 2, 20);
        proj = mult(proj,eye);
        this.gl.uniformMatrix4fv(this.projLoc, false,flatten(proj));
    } 

  • Note, the frustum is fixed.
  • Messing with the frustum will change the view dramatically.
  • But you can think of this as just moving the box in front of you.
• So To move in space I need to change the values of the camera.
• I am going to go to a different coordinate system called spherical coordinates
  • This is a way to represent 3 space.
  • A distance and two angles are used.
  • The first angle is the angle from the x axis in the xy plane.
  • The second angle is the angle in from that point in the yz plane.
  • The distance is the radius of the sphere on which we want the point.
• In my mind, this is an extension of polar coordinates.
  • $x = r cos(\theta) sin(\phi)$
  • $y = r cos(\theta) sin(\phi)$
  • $z = r cos(\phi)$
• We will swap the role of y and z.
• My general plan is to
  • Keep the camera position in Cartesian coordinates in modeling space
  • Keep the angles $ \theta, \phi$ as variables.
  • To rotate
    • Increment or decrement $ \theta, \phi$ as needed.
    • Recalculate the at position.
  • When I want to move.
    • Calculate an offset from the current position.
    • Update the camera position by that offset
    • Recalculate the at position.
• Note in this world,
  • I step to where I am looking.
  • I step the same amount ahead of me that I am looking.
  • I don't need to do that, but that is probably your problem, not mine.
• So how do I compute the new "target" position
  • Pretend the camera is at the origin.
  • Using $ \theta, \phi$ and a fixed step size, pretend they are spherical coordinates.
  • Add this offset to the current camera position to find the new camera position.
  • Add this offset to the new camera position to find the new at position.
• I really should update the up vector
  • If up and at are the same, I have a problem.