Mapping 3D point to cone surface using perpendicular line

In summary, the solution for obtaining u1 is achieved by solving simultaneous equations of perpendicular straight line functions (m1 and m2) in the top diagram, not through the use of m3 as shown in the bottom diagram.
  • #1
mamort
6
0
Can someone please look at the diagram below and tell me how u1 is obtained. If it is through the use of m3 please explain how the gradient m3 is obtained.

Geometric Problem (v1.3).jpg
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 
  • #3
Thanks for monitoring this problem, I have now found the solution which is achieved by solving simultaneous equations of both straight line functions (m1 and m2) that are perpendicular in the top diagram above. The bottom diagram is NOT how the solution is achieved.
 

FAQ: Mapping 3D point to cone surface using perpendicular line

1. What is the purpose of mapping a 3D point to a cone surface using a perpendicular line?

Mapping a 3D point to a cone surface using a perpendicular line is a method used in computer graphics and 3D modeling to accurately represent the position of a point on a cone. This allows for more realistic and precise rendering of cone-shaped objects in 3D environments.

2. How does the mapping process work?

The mapping process involves finding the closest point on the cone surface to the given 3D point. This is done by extending a perpendicular line from the 3D point to the cone, and then finding the intersection of this line with the cone's surface. The resulting point is the mapped point on the cone surface.

3. What are the benefits of using perpendicular line mapping?

Perpendicular line mapping allows for more accurate representation of cone shapes in 3D, as it takes into account the unique curvature of the cone's surface. This method also works for any point on the cone, regardless of its position or orientation.

4. Are there any limitations to this mapping technique?

One limitation of mapping 3D points to cone surfaces using perpendicular lines is that it only works for perfect cones, meaning cones with perfectly circular bases and constant slope. It may not give accurate results for irregular or distorted cone shapes.

5. How is this mapping technique useful in real-world applications?

This mapping technique is commonly used in computer graphics and 3D modeling for various applications, such as video game development, animation, and virtual reality. It allows for more realistic and precise rendering of cone-shaped objects, which can enhance the overall visual experience for users.

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