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

In summary, to draw a tilted circle, you need to use the equations for a 3D circle, with the radius and angle parameters, and then transform the orientation using a direction cosine matrix. Additional resources for understanding this process can be found in introductory texts on mechanics or aero, as well as online.
  • #1
rromanowski
1
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:
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  • #2

1. What is a parametric equation for a 3D circle that is off-axis?

A parametric equation for a 3D circle that is off-axis is a set of equations that represent the x, y, and z coordinates of points on the circle in terms of one or more parameters. These equations can be used to graph the circle and calculate the coordinates of any point on the circle.

2. How is the parametric equation for a 3D circle that is off-axis different from a regular 3D circle equation?

The parametric equation for a 3D circle that is off-axis takes into account the center point and radius of the circle, as well as the angle of rotation or tilt of the circle in 3D space. This allows for a more precise representation of the circle's position and orientation compared to a regular 3D circle equation.

3. What are the benefits of using a parametric equation for a 3D circle that is off-axis?

The main benefit of using a parametric equation for a 3D circle that is off-axis is that it allows for more flexibility in representing the circle's position and orientation. It also makes it easier to manipulate and calculate points on the circle, as the equations can be easily adjusted to fit different scenarios.

4. Can a parametric equation for a 3D circle that is off-axis be used for any off-axis circle?

Yes, a parametric equation for a 3D circle that is off-axis can be used for any off-axis circle, regardless of its size or orientation. As long as the center point, radius, and angle of rotation/tilt are known, the equation can be adjusted to fit the specific circle.

5. How is a parametric equation for a 3D circle that is off-axis derived?

The parametric equation for a 3D circle that is off-axis is derived using trigonometric functions and the Pythagorean theorem. By setting up equations for the x, y, and z coordinates of points on the circle and solving for the parameters, a general parametric equation can be found. This equation can then be adjusted for different scenarios to represent different off-axis circles.

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