![]() The three points of any triangle will lie on a unique circle.ģ)My primary focus was to see if anyone had a mathematical (vs. We are only looking for a radius and the ceenter of that radius, as determined by the three XYZ defined points (non-colinear).Ģ) The 3 pts do define a triangle on a plane. But we are not looking for anything spherical. Just to clarify on some of the issues / questions.ġ) I know we need 4 points to define a sphere. Where RE: Find circle radius & circle center in 3D from (3) XYZ pts DrMetal (Materials) ![]() X,Y,Z are the unknown coordinates of the sphere centerĤ equations and 4 unknowns should get the solution unless the 4 points are co-planer. You get it obviously by finding a 3rd plane that bisects the line from that 4th point to any of the other points the intersection of the 3 planes so formed is the center. Now you need a 4th point in space to determine that unique sphere. Now since the intersection of these planes is a LINE and EVERY point on that line is equidistant to the 3 points so that, there is no unique center and therefore no unique sphere. Then find the plane of the bisector of point 2 and point 3. The center is found by first finding the plane that is the bisector of any two points,say point 1 and point 2. Thanks, MWP RE: Find circle radius & circle center in 3D from (3) XYZ pts GregLocock (Automotive) 24 Jun 09 04:08įirst off, 3 points in space do not determine the surface of a unique sphere. I have seen most of them, and still am stuck on this. being directed to one of the web solutions. I'd prefer to have a detailed step-by-step solution vs. I'd prefer an approach that could be put into a spreadsheet to make reiterative calcs go quickly. These are special alloy pipes $25k each, so we want to be sure we have the correct 2D bend radius before we bend them. We need to be able to determine the TRUE bend radius of the pipes. We have several drawings with bent pipes in 3D where we have only THREE 3D points given to us. With as much time as we have spent on this problem, we would be happy to compensate someone for their time to solve this for us. Seems when I try the double elimination (or substitution) of variables approach, I keep coming up with unsolvable, or meaningless equations. Is it possible to solve this mathematically with (3) simultaneous quadratic equations? Or do I need a 4th equation, determinates, etc?. Seems I keep going in mathematical circles (no pun intended) with a modified Excel approach with the three quadratic equations. But I can't get it to work in 3D with a similar spreadsheet approach with THREE variables (i.e. I can do this easily from three points in 2D, in Excel using three simultaneous equations with TWO variables (i.e. I have searched the web extensively, and found lots of proposed solutions, but my college math is quite rusty and after several days, I still can not come up with the correct detailed solution. Question: Can someone provide a mathematical step by step procedure to calculate and determine a circle radius and the center point coordinates from three GIVEN 3D points with X-Y-Z coordinates? FIND: Radius of circle on those 3 points & Circle center co-ordinatesBookmark: GIVEN: X-Y-Z coordinates of 3 points in 3D space.
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