Transformation Matrix from x-axis

In summary, the given parametric equation represents a cone with height h and base radius a on the x-axis. To transform it to lie on the theta and phi axis, a new set of equations is used with the coordinates x1, y1, and z1 being determined by the values of theta and phi for all u and v.
  • #1
Philosophaie
462
0
I have a Parametric Equation for a Cone:

x=u
y=cos(v)*a*(u-h)/h
z=sin(v)*a*(u-h)/h

where:
h is height of the cone
a is the Radius of the Base
u goes from 0 to h
v goes from 0 to 2*pi

This cone lies on the x-axis. I need it to lie on the theta and phi axis. This is what I came up with to transform it:

|x1| |cos(theta)*cos(phi) sin(phi) sin(theta)*cos(phi) | |x|
|y1| = |sin(theta)*cos(phi) cos(theta)*cos(phi) sin(phi) | = |y|
|z1| |sin(phi) sin(theta)*cos(phi) cos(theta)*cos(phi)| |z|
 
Last edited:
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  • #2
What do you mean by "the theta and phi axis"?
 
  • #3
Originally at (r, 0 ,0) transform to (r, theta, phi) for all u and v.
 

1. What is a transformation matrix from the x-axis?

A transformation matrix from the x-axis is a mathematical representation of a transformation applied to a vector or set of coordinates in a 3-dimensional space. It is used to rotate, scale, or translate objects in computer graphics and physics simulations.

2. How is a transformation matrix from the x-axis calculated?

A transformation matrix from the x-axis is typically calculated by using a combination of trigonometric functions and linear algebra operations. The exact formula will vary depending on the specific transformation being applied.

3. What is the purpose of using a transformation matrix from the x-axis?

The purpose of using a transformation matrix from the x-axis is to simplify the process of transforming objects in 3-dimensional space. By using a matrix, multiple transformations can be applied simultaneously, making it a more efficient method compared to using individual operations.

4. How is a transformation matrix from the x-axis used in computer graphics?

In computer graphics, a transformation matrix from the x-axis is used to manipulate the position, orientation, and size of objects on the screen. This allows for the creation of complex and realistic 3-dimensional images and animations.

5. Can a transformation matrix from the x-axis be applied to 2-dimensional objects?

Yes, a transformation matrix from the x-axis can be applied to 2-dimensional objects as well. In this case, the z-coordinate of the object is set to zero, resulting in a 2-dimensional transformation. This is commonly used in computer graphics to rotate, scale, or translate 2-dimensional images and shapes.

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