Helpers.cpp File Reference

Code for helper functions. More...

#include <algorithm>
#include <sstream>
#include "Helpers.h"

Go to the source code of this file.

Functions
const float	spline3 (float t)
	Cubic spline. More...
const float	spline5 (float t)
	Quintic spline. More...
const float	lerp (float t, float a, float b)
	Linear interpolation. More...
const float	clamp (float a, float x, float b)
	Clamp between two values. More...
std::wstring	to_wstring_f (float x, size_t n)
	Float to fixed precision wstring. More...
const bool	isPowerOf2 (size_t n)
	Power of 2 test. More...

Function Documentation

clamp()

const float clamp	(	float	a,
		float	x,
		float	b
	)

Clamp between two bounds.

Parameters

a	Lower bound, assumed to be less than \(\mathsf{b}\).
x	Value to be clamped.
b	Upper bound, assumed to be greater than \(\mathsf{a}\).

Returns

Closest value to \(\mathsf{x}\) between the lower and upper, bounds (inclusive), that is, \(\mathsf{\max(a, \min(x, b))}\).

Definition at line 67 of file Helpers.cpp.

isPowerOf2()

const bool isPowerOf2

(

size_t

n

)

Test whether an unsigned integer is a power of 2. This is a sneaky one. It relies pm the fact that n is a power of 2 iff n is nonzero and n & (n - 1) is zero. To see this, note that if \(n = 2^k\), then the binary representation of \(n\) is a one followed by \(k\) zeros and that of \(n-1\) is a zero followed by \(k\) ones. Clearly the bit-wise conjunction of the two is zero. Conversely, if \(n\) is not a power of two, then the binary representations of \(n\) and \(n-1\) will share one-bits in the same position so their conjunction will be non-zero.

Parameters

n

A number.

Returns

true if the parameter is a power of 2.

Definition at line 94 of file Helpers.cpp.

lerp()

const float lerp	(	float	t,
		float	a,
		float	b
	)

Linear interpolation between two values.

Parameters

t	Interpolation fraction, assumed to be in \([0,1]\).
a	Lower value.
b	Upper value.

Returns

A \(\mathsf{t}\) fraction of the way between \(\mathsf{a}\) and \(\mathsf{b}\), that is, \(\mathsf{(1-t)a + tb}\).

Definition at line 56 of file Helpers.cpp.

spline3()

const float spline3

(

float

t

)

Compute the cubic spline of a parameter \(t\), that is, \(3t^2 - 2t^3\).

Parameters

t	Parameter.

Returns

Cubic spline of parameter.

Definition at line 36 of file Helpers.cpp.

spline5()

const float spline5

(

float

t

)

Compute the quintic spline of a parameter \(t\), that is, \(10t^3 - 15t^4 + 6t^5\).

Parameters

t	Parameter.

Returns

Quintic spline of parameter.

Definition at line 45 of file Helpers.cpp.

to_wstring_f()

std::wstring to_wstring_f	(	float	x,
		size_t	n
	)

Convert a floating point number into a fixed precision wide string.

Parameters

x	A floating point number.
n	Number of digits after the decimal point.

Returns

Fixed precision string.

Definition at line 76 of file Helpers.cpp.