Finding points on a cylinder in 3d room c#

Question

Example Image here I am trying to find a way to calculate points on my cylinders top circle surface. My situation looks like this, I have a vector which is defining my cylinders direction in 3d room. Then I already calculated me a perpendicular vector with

Vector3.Cross(vector1, vector2)

Now I use the diameter/2 to calculate the point which is lying on the edge of the circular top surface of my cylinder. Now I want to rotate my vector always 90 degrees in order to get 4 points on the edge of the surface. All the 4 vectors defining them should be perpendicular to the cylinders direction. Can you help me how I can rotate the first perpendicular to achieve this?

I already tried:

Matrix4x4.CreateFromAxisAngle(vectorcylinderdirection, radiant)

Then I calculated again cross product but it doesnt work like I want to.

Edit:

        public static void calculatePontsOnCylinder()
    {

        //Calculate Orthogonal Vector to Direction
        Vector3 tCylinderDirection = new Vector3(1, 0, 0);
        Vector3 tOrthogonal = Vector3.Cross(tCylinderDirection, new Vector3(-tCylinderDirection.Z,tCylinderDirection.X,tCylinderDirection.Y));
        Vector3 tNormOrthogonal = Vector3.Normalize(tOrthogonal);

        //Calculate point on surface circle of cylinder
        //10mm radius
        int tRadius = 10;
        Vector3 tPointFinder = tNormOrthogonal * tRadius;

        //tPointFinder add the cylinder start point
        //not yet implemented

        //now i need to rotate the vector always 90 degrees to find the 3 other points on the circular top surface of the cylinder
        //don't know how to do this
        // I thought this should do it
        Matrix4x4.CreateFromAxisAngle(tCylinderDirection, (float)DegreeToRadian(90));



    }

    private static double DegreeToRadian(double angle)
    {
        return Math.PI * angle / 180.0;
    }

In the picture you can see a example, the vector1 is what I need, always rotated 90 degrees and vector2 would be my cylinder direction vector

I possibly have found the correct formula:

Vector3 tFinal = Vector3.Multiply((float)Math.Cos(DegreeToRadian(90)), tPointFinder) + Vector3.Multiply((float)Math.Sin(DegreeToRadian(90)), Vector3.Cross(tCylinderDirection, tPointFinder));
        Vector3 tFinal180 = Vector3.Multiply((float)Math.Cos(DegreeToRadian(180)), tPointFinder) + Vector3.Multiply((float)Math.Sin(DegreeToRadian(180)), Vector3.Cross(tCylinderDirection, tPointFinder));
        Vector3 tFinal270= Vector3.Multiply((float)Math.Cos(DegreeToRadian(270)), tPointFinder) + Vector3.Multiply((float)Math.Sin(DegreeToRadian(270)), Vector3.Cross(tCylinderDirection, tPointFinder));

Interesting is that if I try it with (1,1,0) as cylinder direction it gives me correct directions but the length is different for 90 degrees and 270.

Answer 1

Here is the code that should solve your problem assuming that the input requirements are satisfied.

        float zCutPlaneLocation = 20; // should not get bigger than cylinder length
        float cylinderRadius = 100;
        Vector3 cylinderCenter = new Vector3(0, 0, 0); // or whatever you got as cylinder center point, given as Vector3 since Point type is not defined

        // will return 360 points on cylinder edge, corresponding to this z section (cut plane),
        // another z section will give another 360 points and so on
        List<Vector3> cylinderRotatedPointsIn3D = new List<Vector3>();

        for (int angleToRotate = 0; angleToRotate < 360; angleToRotate++)
        {
            cylinderRotatedPointsIn3D.Add(GetRotatedPoint(zCutPlaneLocation, angleToRotate, cylinderRadius, cylinderCenter));
        }

         ....

       private static Vector3 GetRotatedPoint(
        float zLocation, double rotationAngleInRadian, float cylinderRadius, Vector3 cylinderCenter)
       {
        Vector2 cylinderCenterInSection = new Vector2(cylinderCenter.X, cylinderCenter.Y);

        float xOfRotatedPoint = cylinderRadius * (float)Math.Cos(rotationAngleInRadian);
        float yOfRotatedPoint = cylinderRadius * (float)Math.Sin(rotationAngleInRadian);

        Vector2 rotatedVector = new Vector2(xOfRotatedPoint, yOfRotatedPoint);
        Vector2 rotatedSectionPointOnCylinder = rotatedVector + cylinderCenterInSection;

        Vector3 rotatedPointOnCylinderIn3D = new Vector3(
                                                    rotatedSectionPointOnCylinder.X,
                                                    rotatedSectionPointOnCylinder.Y,
                                                    zLocation + cylinderCenter.Z);

        return rotatedPointOnCylinderIn3D;
       }

I just created a console app for this. First part of code should be added in main method. Working with those matrices seems is not that easy. Also I am not sure if your solution works ok for any kind of angle. Here the idea is that the rotated points from cylinder are calculated in a section of the cylinder so in 2D than the result is moved in 3D by just adding the z where the Z section was made on cylinder. I suppose that world axis and cylinder axis are on the same directions. Also if your cylinder gets along (increases) on the X axis, instead of Z axis as in example just switch in code the Z with X.

I attached also a picture for more details. This should work if you have the cylinder center, radius, rotation angle and you know the length of the cylinder so that you create valid Z sections on cylinder. This could get tricky for clockwise/counter clock wise cases but lets see how it works for you.

If you want to handle this with matrices or whatever else I think that you will end up having this kind of result. So I think that you cannot have "all" the rotated points in just a list for the entire cylinder surface, they would depend on something like the rotated points of a Z section on the cylinder.