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I am currently working on a Physics Engine in C++. The Physics Engine is for a sandbox video game. I want to build a powerful physics engine, so therefore, it needs to be very precise.

I have written the following function:

Vector3D* rotationX(double theta);

This function will rotate a vector around the x-axis at theta degrees. My test attempts to rotate the vector <0,1,0> about the x-axis, which should be the vector <0,0,1>. The output is the following vector, which is very close to what it should be: <0,0.000796327,1>.

I am aware of the floor function, but I think this isn't precise enough since my 3-d vector class should be able to handle real numbers; that is, not just integers.

  • You are not handling real numbers. You are not even handling rational numbers. You are handling floating point numbers. If you need to handle rational numbers, you'll need a library for handling arbitrary precision "decimal" numbers. – 94239 Aug 24 at 21:40
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    The result you have is not very close at all. That's not due to rounding error, there is some serious bug in your code. – gnasher729 Aug 24 at 22:01
  • Its best to publish the code. – NoChance Aug 25 at 0:39
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    Have you quantified how precise it needs to be? – No U Aug 26 at 16:50
  • @TKK problems fixed. – Gary Drocella Aug 26 at 16:54
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You have basically the following options:

1.) Do nothing. Maybe the result is precise enough for your use case. Note when using floating point operations, it is quite normal you have to deal with some rounding errors. I would recommend to have a look at What Every Computer Scientist Should Know About Floating-Point Arithmetic.

2.) If your use case involves comparing two vectors for equality, make sure you compare against some "epsilon", where epsilon is about 10^(-3).

3.) Find out why the result is that much imprecise. A rotation involving standard trigonometric functions which uses 64 bit double precision should usually bring results up to a preciseness better than 10^(-10) to my experience.

In between, it became clear (see comments) that in this case the root cause was using 3.14 as an approximation for Pi. It is usually a good idea to use predefined constants for such standard values whenever they are available in the used environment. In C++, for example, one can use the constant M_PI from <math.h> (see this SO post).

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