[mimi0201]

Can anyone please explain the meaning of the sentence "alpha = M_PI/2. - acos(MAX(-1.,MIN(1.,NV_DOT(normal,p->state.V)/MAX(NV_MAG(p->state.V),DPM_SMALL))));".

[`e`]

Where did you get this equation from and what is this equation describing?

The first term, M_PI/2., is simply .

Let's now analyse the second term by expanding the brackets to make some sense of this line of code:

-acos(
	MAX(
		-1.,
		MIN(
			1.,
			NV_DOT(normal,p->state.V)/MAX(NV_MAG(p->state.V),DPM_SMALL)
		)
	)
);

Briefly, these functions are: acos (inverse cosine), max (maximum of a set of values), min (minimum of a set of values), NV_DOT (dot product vector operation), NV_MAG (magnitude of a vector).

"p->state.V" is the velocity vector; could also be accessed with C_U(c,t). DPM_SMALL is a small number.

[mimi0201]

Originally Posted by `e`

Where did you get this equation from and what is this equation describing?

The first term, M_PI/2., is simply .

Let's now analyse the second term by expanding the brackets to make some sense of this line of code:

-acos(
	MAX(
		-1.,
		MIN(
			1.,
			NV_DOT(normal,p->state.V)/MAX(NV_MAG(p->state.V),
			DPM_SMALL
			)
		)
	)
);

Briefly, these functions are: acos (inverse cosine), max (maximum of a set of values), min (minimum of a set of values), NV_DOT (dot product vector operation), NV_MAG (magnitude of a vector).

"p->state.V" is the velocity vector; could also be accessed with C_U(c,t). DPM_SMALL is a small number.

Thank you so much for the explanation, this equation is from DPM udf, determining the angle between wall tangent and the incoming particle. It is hard for me to understand the principle of calculating the angle like why need max and min. Cheers.

[`e`]

The inverse cosine function is real only if evaluated between -1 and 1. The MIN() and MAX() functions restrict the input value to between -1 and 1 to avoid imaginary/garbage numbers as an output.

[mimi0201]

Originally Posted by `e`

The inverse cosine function is real only if evaluated between -1 and 1. The MIN() and MAX() functions restrict the input value to between -1 and 1 to avoid imaginary/garbage numbers as an output.

I think I got it, min() and max() only act to restrict the value from -1 to 1 which suits the input range of acos(), and the actual calculation of incident angle is "NV_DOT(normal,p->state.V)/MAX(NV_MAG(p->state.V)," this equation right?

[`e`]

Have a read of scalar projection to understand the mathematics.

The equation this code is solving:



where is the normal vector of the wall and is the velocity vector of the particle.

Ideally, the corresponding code:

alpha = M_PI/2. - acos(NV_DOT(normal,p->state.V)/NV_MAG(p->state.V));

Except to ensure there are no errors, the coders have restricted the inputs for the acos() function by using MAX() and MIN(). Note that they have used the second MAX() function with DPM_SMALL because if , you'd be trying to divide by zero!

[mimi0201]

Originally Posted by `e`

Have a read of scalar projection to understand the mathematics.

The equation this code is solving:



where is the normal vector of the wall and is the velocity vector of the particle.

Ideally, the corresponding code:

alpha = M_PI/2. - acos(NV_DOT(normal,p->state.V)/NV_MAG(p->state.V));

Except to ensure there are no errors, the coders have restricted the inputs for the acos() function by using MAX() and MIN(). Note that they have used the second MAX() function with DPM_SMALL because if , you'd be trying to divide by zero!

It helps a lot! Cheers!