====== Toolbox functions ======

===== Clamp =====
**Definition**: min(max(f,a),b)

**Call**: hfA_Clamp(f,a,b);

**Parameters**:

f : real value (to be clamped)\\
a : lower boundary of the interval\\
b : upper boundary of the interval

===== Step =====
**Definition**: if f<a return 0 else return 1

**Call**: hfA_Step(f,a);

**Parameters**:

f : real value 
a : real value 

===== Pulse =====
{{http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/images/hfA_Pulse.JPG?200x200&nolink}}
**Definition**: step(f,a)-step(b,f)

**Call**: hfA_Pulse(f,a,b);

**Parameters**:

f : real value 
a : real value 
b : real value 

**Test file**: [[http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/hffiles/hfA_Pulse.hf|hfA_Pulse.hf]]

===== Smooth Step =====
**Definition**: Mapping a value f to [0,1], with a smooth interpolation of 's' between [smin,smax] 

**Call**: hfA_SmoothStep(s,smin,smax,f,fmin,fmax);

**Parameters**:

s : real value 
smin : real value 
smax : real value 
f : real value 
fmin : real value 
fmax : real value 

**Output**: f - value between [0,1], s - value between [smin, smax]

===== Modulo =====
{{http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/images/hfA_modulo.JPG?200x200&nolink}}
**Definition**: a%b

**Call**: hfA_Modulo(a,b);

**Parameters**:

a : lower boundary of the interval
b : upper boundary of the interval

**Test file**: [[http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/hffiles/hfA_Modulo.hf|hfA_Modulo.hf]]

===== Floor =====
**Definition**: integer part of 'a'

**Call**: hfA_Floor(a);

**Parameters**:

a : real value

===== Linear Interpolation =====
{{http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/images/hfA_lerp.JPG?200x200&nolink}} \\
**Definition**: t = (xt-x0)(x1-x0) \\
if(t<0) t = 0 \\
if(t>1) t = 1 \\
c2 = (1-t)*c0+t*(c1)

**Call**: hfA_Lerp(c2,c1,c0,xt,x1,x0)

**Parameters**: \\
xt - point coordinate \\
x0,x1 - Interval in between the interpolation is done \\
c0,c1 - Input array \\

**Output**: \\
c2 : array of values (linear interpolation of c0 and c1)

**Test file**: [[http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/hffiles/hfA_Lerp.hf|hfA_Lerp.hf]]

===== Cubic interpolation =====
{{http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/images/hfA_Cerp.JPG?200x200&nolink}} \\
**Definition**: t = 3xt^2-2xt^2. with xt in [x0,x1] \\
if(t<0) t = 0 \\
if(t>0) t = 1 \\
c2 = (1-t)*c0+t*(c1) 

**Call**: hfA_Cerp(c2,c1,c0,xt,x1,x0)

**Parameters**: \\
xt - point coordinate \\
x0,x1 - Interval in between the interpolation is done \\
c0,c1 - Input array \\

**Output**: \\
c2 : array of values (linear interpolation of c0 and c1)

**Test file**: [[http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/hffiles/hfA_Cerp.hf|hfA_Cerp.hf]]

===== Spline Interpolation =====
{{http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/images/hfA_spline.JPG?200x200&nolink}} \\
**Definition**: Given an array of 3*n values (in the case of rgb attributes), and given an interval [t0,t1], a spline interpolation is performed to obtain the resulting set of attributes

**Call**: HFA_Spline(s,c,t,t0,t1)

**Parameters**: \\
s - Output array (attributes) \\
c - Input array (attributes) \\
t - Real value \\
t0,t1 - Real values, interval \\

**Output**: \\
s : array of values (attributes) interpolated from the array c

**Test file**: [[http://www.hyperfun.org/HF2/Language/Library/Attri_Lib/hffiles/HFA_Spline.hf|HFA_Spline.hf]]