Ways to identify faces of a 3D form obscured by other surfaces (undetectable from a specific viewpoint)

Question

Ways to identify faces of a 3D form obscured by other surfaces (undetectable from a specific viewpoint)

Imagine a scenario where we have a 3D cube positioned in a XYS coordinate system. While shapes can vary in complexity, let's begin with a simple cube. We are observing the cube from a distant point at a specific angle to the front face, similar to how a camera gazes at the cube from an angle to all XYZ axes.

How can we programmatically identify invisible faces? In this case, the bottom, left, and back faces are concealed.

javascript three.js 3d

Answer 1

Answer №1

The technique used to eliminate non-visible triangles is known as Backface Culling. It involves projecting three 3D points onto a 2D screen and determining their arrangement as either clockwise or counter-clockwise. By analyzing the direction of the Normal Vector, which either extends into or out of the screen, it can be determined if a triangle is facing the front or back side. Triangles facing the back side are simply discarded.

While this method is straightforward, the challenge arises when dealing with convex/concave 3D polyhedra. In such cases, it becomes complex to ascertain whether a front-facing triangle is obstructed by other triangles within the same structure.

For instance, consider the situation where a rectangle R is positioned behind a U-shaped structure:

+--------+
|        |
|  +--+  |
|  |  |  |  <-- Rectangle R is visible through the U shape
|  |  |  |
+--+  +--+

Here, the task involves determining if the rectangle R is completely obscured by the U shape or if parts of it remain visible by computing the intersections of the two polygons.

As the complexity of polyhedra increases, the algorithm needed to determine visibility also becomes more intricate. Hence, this approach may not be suitable unless real-time performance is not a concern, and it may not necessarily be graphics-related.

In computer graphics, a Z-buffer is commonly employed to render all front-facing triangles, following backface culling. This involves storing the depth values in a buffer and checking the Z values while rendering pixels to determine visibility.

Real-time visibility analysis, particularly at 60 Hertz, is challenging without rendering all triangles using Z-buffer on current GPU hardware. While CPU-based algorithms can perform visibility checks, they are considerably complex and require extensive study to implement effectively.

Backface culling provides a quick and rudimentary solution, while visibility checking is a highly intricate process that may necessitate external tools. The Z-buffer method, on the other hand, involves rendering triangles and is not primarily an optimization technique for avoiding unnecessary geometry rendering.

Answer 2

The technique used to eliminate non-visible triangles is known as Backface Culling. It involves projecting three 3D points onto a 2D screen and determining their arrangement as either clockwise or counter-clockwise. By analyzing the direction of the Normal Vector, which either extends into or out of the screen, it can be determined if a triangle is facing the front or back side. Triangles facing the back side are simply discarded.

While this method is straightforward, the challenge arises when dealing with convex/concave 3D polyhedra. In such cases, it becomes complex to ascertain whether a front-facing triangle is obstructed by other triangles within the same structure.

For instance, consider the situation where a rectangle R is positioned behind a U-shaped structure:

+--------+
|        |
|  +--+  |
|  |  |  |  <-- Rectangle R is visible through the U shape
|  |  |  |
+--+  +--+

Here, the task involves determining if the rectangle R is completely obscured by the U shape or if parts of it remain visible by computing the intersections of the two polygons.

As the complexity of polyhedra increases, the algorithm needed to determine visibility also becomes more intricate. Hence, this approach may not be suitable unless real-time performance is not a concern, and it may not necessarily be graphics-related.

In computer graphics, a Z-buffer is commonly employed to render all front-facing triangles, following backface culling. This involves storing the depth values in a buffer and checking the Z values while rendering pixels to determine visibility.

Real-time visibility analysis, particularly at 60 Hertz, is challenging without rendering all triangles using Z-buffer on current GPU hardware. While CPU-based algorithms can perform visibility checks, they are considerably complex and require extensive study to implement effectively.

Backface culling provides a quick and rudimentary solution, while visibility checking is a highly intricate process that may necessitate external tools. The Z-buffer method, on the other hand, involves rendering triangles and is not primarily an optimization technique for avoiding unnecessary geometry rendering.

Answer 3

Answer №2

If you are dealing with shapes that can have arbitrary forms, one effective method to consider is utilizing ray casting. For more information on ray casting, you can visit this link: https://en.wikipedia.org/wiki/Ray_casting.

Essentially, the approach involves casting rays (vectors) throughout your scene and determining where these rays intersect with your object. This process can be carried out using basic mathematical calculations. When a ray intersects with multiple points, the first intersection point indicates visibility, while subsequent hits occur on invisible surfaces.

In my own work, I have developed a path tracer that employs ray casting to identify visible elements for a camera: https://github.com/jo-va/hop. You are welcome to explore the code and leverage it for your own project!

I hope this information proves beneficial to you.

Answer 4

If you are dealing with shapes that can have arbitrary forms, one effective method to consider is utilizing ray casting. For more information on ray casting, you can visit this link: https://en.wikipedia.org/wiki/Ray_casting.

Essentially, the approach involves casting rays (vectors) throughout your scene and determining where these rays intersect with your object. This process can be carried out using basic mathematical calculations. When a ray intersects with multiple points, the first intersection point indicates visibility, while subsequent hits occur on invisible surfaces.

In my own work, I have developed a path tracer that employs ray casting to identify visible elements for a camera: https://github.com/jo-va/hop. You are welcome to explore the code and leverage it for your own project!

I hope this information proves beneficial to you.

Ways to identify faces of a 3D form obscured by other surfaces (undetectable from a specific viewpoint)

Answer №1

Answer №2

Similar questions

Utilize JavaScript to load images at random within a Qualtrics loop and merge block

Retrieving embedded documents from Mongoose collections

The function onKeyDown is not working properly

Create a PDF document and provide a reply

It is impossible to add a promise's value to an array

How can I use AngularJS to show a JSON value in an HTML input without any modifications?

"Efficiently setting up individual select functions for each option in a UI select menu

Trouble with Setting Up the Email Address for the 'File a Complaint' Form in WordPress

Populating a div with letter-spacing

What could be causing my JavaScript loop to replace existing entries in my object?

Achieve the appearance of a galloping horse using JQuery

Each time the website refreshes, Object.entries() rearranges the orders

Developing a Prototype for an Angular Directive

Loss of image quality when utilizing Next/Image in NEXT JS

Creating linear overlays in Tailwind CSS can be achieved by utilizing the `bg-gradient

Using JSON parsing to extract an integer as the key in JavaScript

How to Utilize findIndex to Validate the Presence of Elements in an Array of Objects using TypeScript

Tips for adding additional text to c3.js Regions

url-resettable form

Unravel the encoded string to enable JSON parsing