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I am looking for a (can be a paid version) software that allows me:

  1. to render a 2D cross section of a given 3D model, cut at any particular plane

  2. the 2D cross section containing enough information to allow me to do line tracing

  3. the software should have an API that can allow me to render the cross section drawing directly from a C++/C# programmed GUI (such as WinForms).

To elaborate, I am actually working on a project that deals with ultrasound testing. Essentially my program takes input parameters such as the thickness, radius, length and angle of intersection between two pipes. So I will have full representation in terms of parametric equations for the pipes (as opposed to a point cloud-like format).

What I am looking for is a way to visualise the ultrasound beam paths within the 3D model.

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I think I'd look at OnShape for CAD-like and parametric 3D modeling, but for the kind of visualization you're looking at, I think you may want to look at Blender, or any other of the major DCC 3D apps out there - so Maya, modo, 3DS, Cinema 4D... but given Blender's free and open source heritage, as well as its extensibility, not to mention both the Blender project having a well documented API AND a gazillion coders working on the project all the time... that's where I'd start were I you.

FWIW: I use modo as my main DCC tool, but that's down to preference and range of tools I specifically need doing mostly architectural visualisations.

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