How to Calculate 3D Fillet Tangent Points and Center in Excel?

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SUMMARY

This discussion focuses on calculating the tangent points and center of a fillet circle in 3D space using known coordinates P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), and P3-(X3, Y3, Z3) with a specified radius R. The solution involves deriving the equations of the lines connecting the points and utilizing the angle bisector to locate the center of the fillet circle. The participants emphasize the need for a clear mathematical approach that can be implemented in Excel, highlighting the importance of understanding the geometric relationships between the points.

PREREQUISITES
  • Understanding of 3D coordinate geometry
  • Knowledge of trigonometry and angle bisectors
  • Familiarity with Excel for implementing mathematical equations
  • Basic concepts of circles and tangents in geometry
NEXT STEPS
  • Research the derivation of equations for lines in 3D space
  • Learn how to calculate angle bisectors in three dimensions
  • Explore methods for implementing geometric calculations in Excel
  • Study the properties of circles and tangents in 3D geometry
USEFUL FOR

This discussion is beneficial for students and professionals in mathematics, engineering, and computer-aided design (CAD) who require geometric calculations for projects involving 3D modeling and design.

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Homework Statement



I have 3 known point, with coordinate P1-(X1, Y1, Z1), P2-(X2, Y2, Z2), P3-(X3, Y3, Z3).

straight line is draw from P1 to P2, P2 to P3. they are "not" collinear.

I would like to fit a round fillet to the conner with a "Known" radius of R, and I would like to know the coordinate of the 2 tangent point and the center of the fillet circle.

How can I calculated it in 3D coordinate with a sample single equation for each of the tangent point and center of the fillet, so I can use in Excel. Is this possible?

Please help as I need to complet this for my project.

Homework Equations





The Attempt at a Solution

 
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Is this a math project or a machining project?

Can you write down the equations of the 2 lines? From the equations, can you find the angle between them? Does noticing that the center of the circle lies on the angle bisector help (there's a right triangle of known angles that can be drawn)?
 

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