Jump to content
  • Advertisement
Sign in to follow this  

Circumcenter calculation

This topic is 4469 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Hi everyone. I am trying to calculate the circumcenter of a triangle in 3D space. The way I see it, the geometric properties of the circumcenter can be used to compute its coordinates. The property I have in mind is that the circumcenter of a triangle is the point of intersection of all the three lines that: a) are perpendicular to the triangle's sides and b) intersect the triangle's sides at their midpoint This means that if A, B and C are the triangle's vertices, O the circumcenter and: 1) D the midpoint of A, B 2) F the midpoint of B, C 3) G the midpoint of C, A then if must hold that: (O - D) dot (A - B) = 0 (O - F) dot (B - C) = 0 (O - G) dot (C - A) = 0 The three equations above have 3 unknowns each (the x, y and z coordinates of the circumcenter O) and, therefore, present a solvable system of linear equations. The problem is that the coefficient matrix of the above system has determinant equal to 0 and cannot be inverted. Can someone please explain why this is so and perhaps present an algorithm for the calculation of a 3D triangle's cicrumcenter? Thanks.

Share this post

Link to post
Share on other sites
Sign in to follow this  

  • Advertisement

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!