Parametric equation for 3D circle that's off-axis

  • Context: Undergrad 
  • Thread starter Thread starter rromanowski
  • Start date Start date
  • Tags Tags
    3d Circle Parametric
Click For Summary
SUMMARY

The discussion focuses on deriving a parametric equation for a 3D circle tilted at an angle θ from the Y-axis while maintaining its center at the origin. The current equations used are x = r * sin(u) * cos(v), y = r * sin(v), and z = r * cos(u) * cos(v), where r is the radius, u ranges over a full circle, and v ranges from -π/2 to π/2. To achieve the desired tilt, a direction cosine matrix must be applied to transform the sphere's orientation. This transformation is essential for accurately representing the tilted circle in 3D space.

PREREQUISITES
  • Understanding of parametric equations in 3D geometry
  • Familiarity with direction cosine matrices
  • Basic knowledge of trigonometric functions
  • Introductory mechanics or aerospace concepts
NEXT STEPS
  • Research direction cosine matrices for 3D transformations
  • Learn about Euler angles and their applications in 3D rotations
  • Explore advanced parametric equations for complex shapes
  • Study the link provided for kinematics and rotations: http://www.ece.unb.ca/COBRA/Resources/Kinematics,%20Rotations%20and%20Euler%20Angles.pdf
USEFUL FOR

This discussion is beneficial for mathematicians, engineers, and computer graphics developers who are working on 3D modeling, simulations, or any application requiring the representation of tilted geometrical shapes in three-dimensional space.

rromanowski
Messages
1
Reaction score
0
Hi.

I want to know the equation to draw a circle that's a bit tilted. Imagine a 3D circle that's parallel with the Y axis. Now I want to take that circle and have its center cross through the origin still, but I want it to be θ degrees titled from the Y Axis.

I'm using the following equations right now:
x = r * sin(u) * cos(v)
y = r * sin(v)
z = r * cos(u) * cos(v)

where r = radius, u ranges over full circle, v ranges from -pi/2 to pi/2

Thanks,
Ryan
 
Last edited:
Physics news on Phys.org

Similar threads

Undergrad Geometry and algebraic equations
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Circumference of a circle on a spherical surface
  • · Replies 7 ·
Replies
7
Views
6K
Undergrad Testing my knowledge of differential forms
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Finding Minimal Mean Distance Curves on the Unit Sphere
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Show the envelope of circles around a circle is a cardioid
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Torus parametrization and inverse
  • · Replies 1 ·
Replies
1
Views
3K
Graduate Is this a valid parametrization of the torus?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Creating a Vector Field from a 3D Parametric Equation
  • · Replies 2 ·
Replies
2
Views
3K
Undergrad 3D geometry: parametric equation and tangents
  • · Replies 1 ·
Replies
1
Views
2K
High School Question about the limits of integration in a change of variables
  • · Replies 2 ·
Replies
2
Views
3K