3D Line-Plane Clipping

Hi ​@paetzold_s ,

I think a mathematical solution will be required. Consider these properties of a plane and a line segment. 

• n (nx, ny, nz) - normal vector of the plane
• q (xq, yq, zq) - a point on the plane
• p0 (x0, y0, z0) - an end point of the line segment
• p1 (x1, y1, z1) - another end point of the line segment

Then, perform these vector operations.

• v0 (vx0, vy0, vz0) = (x0 - xq, y0 - yq, z0 - zq) - 3D vector from q to p0
• v1 (vx1, vy1, vz1) = (x1 - xq, y1 - yq, z1 - zq) - 3D vector from q to p1
• dp0 = nx x vx0 + ny x vy0 + nz x vz0 - dot product of n and v0
• dp1 = nx x vx1 + ny x vy1 + nz x vz1 - dot product of n and v1 

The condition for the plane and the line segment intersect is,

• (dp0 < 0 and 0 < dp1) or (0 < dp0 and dp1 < 0), i.e. dp0 x dp1 < 0

In FME Workspace, you can use PlanarityFilter transformer (Expose Surface Normal: Yes) to calculate n (nx, ny, nz) : normal vector of a surface and q (xq, yq, zq) : coordinates of a point on the surface.

See the attached workspace that shows how you can implement the logic above to determine if a triangulated surface and a polyline are intersected. It could not be so efficient, but at least better than the solid approach you tried, I think.

Note: Assuming that any triangle face is not vertical to the XY plane and an end point of a line is not on the plane. If there is a such condition, additional processes will be required.