Math Is Fun Forum

Many thanks Bob for all your efforts!

All points are in the first quadrant, but I belief there is still a issue with the first approach regarding detrmining whether and angle is for example +225 or - 135, correct?

Yor second solution contains a lot of Math specific terminology and syntax. I must admit, all that is a bit rusty over here : ). I have to go away for a couple of weeks, when I am back I will see if I can get this to work!

Thanks again!

Thanks for replying bobbym!

Yes, it does pass through all control points. The formula I use calculates the curve between 2 control points by using 2 outer control points. So each curve between 2 control points is based on the position of 4 control points. That said, inserting a control point (even if exactly on the current spline shape) will lead to a different shape! Something I do not want to happen.

Thanks John, I quickly looked at the examples and it seems like a good start. But after thinking more about it I am not sure if typical spline interpolation is what I need?

Please look at the example below. Connecting 3 points results in something like in figure 1 with spline interpolation. Connecting 4 points results in something like figure 2 below. This is not what I need. In my case I am adding points constantly and I do not want the tangent (this is what it is called if I am right?) of the last added point to change (C in figure 2) . The angle at point C should remain the same like in figure 3. The rotation at point D should probably depend on the angle between BC and BD and the distance between CD. Then while interpolation over a timespan I need to find the points on the curve between each 2 points.

Is this indeed a type of Spline interpolation or is there another way to do this?

Thanks a lot guys, I got it working!

Many thanks luca-deltodesco. I read your reply this morning and did a quick test. It didn't work but I have to do more tests. I just wanted to say thanks a lot for your big post.

Just to be sure,  I have never seen this operator  ~=~

Is it like !=   
?

There is is still no 100% clear answer to this but all of us, including real DirectX experts online, think it is YXZ (Y > up, X > right, Z > forward) because all functions related to this have YawPitchRoll in it which basically stands for YXZ (not sure if this is the same in maths terminology?).

I did a test with 2 meshes. mesh1 by default rotated on all 3 axis in one call. Mesh 2 rotated by each axis individually at a time. The order does not influence the end rotation. Mesh 2 always ends up exactly like Mesh 1.

Perhaps this is more complicated then I thought. The directx wrapper has a Mesh SetRotation function for all 3 axis. My Thoughts were, a normal vector points in a certain direction depending on the x,y and z values.  So it should be possible to calculate the angles this vector makes with the x,y and z axis. As this is a landscape/mesh positioning issue my thoughts were also that horizontal rotation of the mesh (y-axis) is not related to the normal vector but depends on the direction the mesh should point at.  So needed are the x and z rotation angles to align the mesh with the landscape at a specific position. Is this relevant information, or am I completely lost here? I don't know about the order of rotations, perhaps this is something I should experiment with when I have a basic idea of how to solve this issue?

I am using pascal (delphi). I read many things about sin and cos. Some saying it is expensive while others did tests and found that it was indeed faster or at least something similar as using a lookup table. I think I should test this myself as I am already using quite a lot of sin and cos in my program.

Well if indeed this is what I should use then I should be able to get it working, thanks again!