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In 2D you can specific an angle range such as [-45 to +45] and clamp a 2D direction vector within that angle range. I want to have something similar for 3D. I want to specify the allowed directional range as a center directional axis with a local y-axis range and a local x-axis range and clamp an arbitrary 3D directional vector within that range. How do I do that?

For example, I want to specify a angle range as axis (1,0,0) with [-30 to 30] as the local y-axis angle angle and [-10 to 10] as the local x-axis range. So that something like (0.95,0.1,0.1).normalized() would not be changed but (-1,0,0) would be clamped to an appropriate vector.

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  • \$\begingroup\$ Are the angle ranges always symmetrical? Is there a minimum/maximum on the ranges? What is the desired result for (-1,0,0)? \$\endgroup\$
    – Jon
    Commented Mar 14, 2016 at 6:51
  • \$\begingroup\$ a cone is good or it has to be a pyramid ? the cone is much easier, you just have a scalar product to make. the pyramid, hm... a 4x4 matrix ? it's equivalent to a view frustum so all projection math should apply \$\endgroup\$
    – v.oddou
    Commented Mar 17, 2016 at 1:18

1 Answer 1

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Assuming your pyramid is defined by a direction vector, an up vector (for the general case, that the pyramid is rotated, it probably defaults to (0, 1, 0)) and two angles maxPitch and maxYaw, I came up with the following solution (in c++, but easily translateable to other languages):

class ViewingPyramid {
    private:
        Vector3 direction, up, right;
        float maxYaw, maxPitch;

    public:
        ViewingPyramid(Vector3 dir, Vector3 up, float yawmax, float pitchmax) :
            direction(Vector3::Normalize(dir)),
            up(Vector3::Cross(direction, Vector3::Normalize(Vector3::Cross(up, direction)))),//Getting a rectangular, orthogonal up vector
            right(Vector3::Cross(direction, this->up))
        {}

        Vector3 Clamp(Vector3 dir) {
            Vector3 abc = getSolutions(right, up, direction);

            Vector3 xz = Vector3::Normalize(dir - abc.Y*up);
            float yaw = Math::Clamp(Vector3::Angle(direction, xz), -maxYaw, maxYaw);

            Vector3 yz = Vector3::Normalize(dir - abc.X*right);
            float pitch = Math::Clamp(Vector3::Angle(direction, yz), - maxPitch, maxPitch);

            Vector3 res = direction;
            Quaternion qYaw = Quaternion::CreateFromAngleAxis(up, yaw);
            Quaternion qPitch = Quaternion::CreateFromAngleAxis(right, pitch);
            res *= qYaw;
            res *= qPitch;

            return res;
        }
    };

As you can see, it relies on some prebuilt math functions, which should mostly be easy to implement. I did not test it, because I don't have getSolutions implemented in my simple math library, but I'm pretty confident this works as intended. You can use whatever library you want (For example Eigen in C++) for math functions, or implement your own. The most complicated part is the getSolutions function, which gets the solutions for the equation dir = a*right + b*up + c*direction.

I hope this helps.

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  • \$\begingroup\$ OP here, but I lost the ability to access the account and I cant comment. Can you elaborate on the implementation of getSolution? I am not clear what it is suppose to do. In any case, I solved my problem by implementing a method to calculate the signed angle between two vectors in a given reference plane. With that, I am able to calculate the local pitch yaw and clamp them to appropriate values. \$\endgroup\$
    – user80667
    Commented Mar 17, 2016 at 0:26
  • \$\begingroup\$ @user80667 getSolutions essentially splits the given directions vector into its local forward-, up- and right-components (It does so by getting the solution to equation I mentioned in the answer). With this you are able to calculate the pitch and yaw angles (like you did) and clamp them. \$\endgroup\$
    – LukeG
    Commented Mar 17, 2016 at 8:50
  • \$\begingroup\$ This works well when either pitch or yaw are zero. However, if both are non-zero it produces a vector outside the pyramid. This is because e.g. as yaw increases, max pitch must decrease. \$\endgroup\$ Commented Apr 25 at 13:53

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