Polyline.TransformAt has inconsistent behavior

[andrewheumann]

Describe the bug A transform taken at t=0 will be oriented totally differently from a transform located at t=0.001. The green volumes are all positioned with transforms from Polyline.TransformAt(t) — see how the start and end volumes are flipped relative to the rest.

To Reproduce Steps to reproduce the behavior: Create a polyline P take P.TransformAt(0) and P.TransformAt(0.001), compare their Y Axes

Expected behavior These orientations should be consistent along the length of the polyline

var polyline = new Polyline(new[] {
              new Vector3(0,0,0),
              new Vector3(20,0,0),
              new Vector3(20,20,0),
              new Vector3(0, 20,0),
            });

            var rectangle = Polygon.Rectangle(5, 10);

            var t1 = polyline.TransformAt(0);
            var t2 = polyline.TransformAt(0.01);
            var mc1 = new ModelCurve(rectangle, null, t1);
            var mc2 = new ModelCurve(rectangle, null, t2);
            var output = new LayoutRoomTestOutputs();
            output.Model.AddElement(mc1);
            output.Model.AddElement(mc2);
            return output;

results in this:

[andrewheumann]

Behavior is ALSO inconsistent between Bezier.TransformAt(0) and Polyline.TransformAt(0)

[ikeough]

Polylines do not follow the same convention as lines where a transform created at a parameter has its Z axis pointing along the curve and the XY plane is perpendicular to the curve. You can see in the image below that the first and last transform are correct in this regard and it's all of the other transforms that are incorrect.

[ikeough]

We want transforms to be consistently oriented along all curves with the X axis to the "right", the Y axis "up" and Z axis pointing backwards along the curve. This provides us a natural mapping of profiles defined in XY to be swept along the curve.

The attached image demonstrates a number of problems:

• The transforms for the "L" polygon are not oriented in the plane of the polygon.
• The transforms at the beginning of the bezier are left-handed.
• The transforms further up the bezier change direction when the direction of curvature changes.

[ikeough]

The solution to the bezier problem is to use FrameType.RoadLike (FrameType.Frenet is the default), which still requires flipping the axes we were doing with cross product: