Скачать или смотреть How to Fix the Plane Equation Calculation from 3 Points in C+ +

Discover how to accurately compute the `Plane Equation` parameters A, B, C, and D using given points in your raytracer project.
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This video is based on the question https://stackoverflow.com/q/63583468/ asked by the user 'Nether Man' ( https://stackoverflow.com/u/6281847/ ) and on the answer https://stackoverflow.com/a/63583650/ provided by the user '1201ProgramAlarm' ( https://stackoverflow.com/u/5231607/ ) at 'Stack Overflow' website. Thanks to these great users and Stackexchange community for their contributions.

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Understanding the Problem: Plane Equation Calculation

In the world of computer graphics and ray tracing, understanding geometric principles is essential. One fundamental concept is the plane equation, usually represented as:

[[See Video to Reveal this Text or Code Snippet]]

In your project, you're trying to derive the coefficients A, B, C, and D for a plane defined by three distinct points in space. Known as points A, B, and C, the task appears straightforward if one understands vector math. However, even when the underlying mathematics seem clear, coding errors can lead to incorrect outputs, particularly for D.

Your current implementation from the problem yields the coefficients for A, B, and C accurately, but the calculated D values seem inconsistent. This discrepancy often stems from using the wrong components of your vectors when determining D.

Solution: Correcting the Calculation of D

Identifying the Mistake

In your implementation, you calculated D as follows:

[[See Video to Reveal this Text or Code Snippet]]

While you have correctly derived A, B, and C, it's crucial to note that the equation for D should be derived entirely from one vector when using the plane's normal vector properties. Mixing components from different vectors leads to the inconsistency you observed.

The Correct Formula for D

The correct way to calculate D should pull data from one of the points, specifically the point A in this case. You should revise your calculation of D to use all components from point A like so:

[[See Video to Reveal this Text or Code Snippet]]

This adjustment ensures that you're expressing the plane's equation in relation to the point you're using, thus resolving the inconsistency in your outputs not just for certain vectors, but for all.

Implementation Example

Here's your updated Plane class constructor:

[[See Video to Reveal this Text or Code Snippet]]

Conclusion

By adjusting the calculation of D to utilize the components from point A, you can ensure that your plane equation generates consistent and correct values. This precise adjustment not only reflects good mathematical practice but also clarifies the logic within your code, making it easier to follow and debug in the future.

With these modifications, you should see a consistent output of the plane equations every time you input different sets of points. Happy coding, and enjoy refining your raytracer project!