/ray/src/lib/numerics/functions.h

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/*
 * lib/numerics/functions.h 
 * 
 * Binary search templates. 
 * 
 * Copyright (c) 2004 by Klaus Sausen (nicolasius § users.sourceforge.net)
 * 
 * This file may be distributed and/or modified under the terms of the 
 * GNU General Public License version 2 as published by the Free Software 
 * Foundation. (See COPYING.GPL for details.)
 * 
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 * 
 */
#ifndef _TemplateLibrary_FUNCTIONS_H_
#define _TemplateLibrary_FUNCTIONS_H_ 1

#include <lib/sconfig.h>
#include <num_math.h>
namespace NUM {


template <class T, class U>
T cosinterp(U x, T v0, T v1) {
    U f;
    f=U(0.5)*(U(1.0)-cos(U(M_PI)*x));
    return v0*(T(1.0)-f)+v1*f;
}

template <class T, class U>
T cubinterp(U x, T v0, T v1, T v2, T v3) {
    T p,q,r,res;
    r=v0-v1;
    p=(v3-v2)-r;
    q=r-p;
    res=v1;
    res+=(v2-v0)*x;
    x*=x;
    res+=q*x;
    x*=x;
    res+=p*x;
    return res;
}

template <class T>
T step (const T a, const T b) {
    return (a>=b)?1.0:0.0;
}

template <class T>
T pulse (const T x, const T a, const T b) {
    return (step(x,a)-step(x,b));
}

template <class T>
T bias(T b, T x) {
    return pow(x,-log2(b)); // optimized to use log2 (Wolfgang)
}

template <class T>
T sbias(T b, T x) {
    return x*T(1.0)/( (T(1.0)-x)*(T(1.0)/(b-T(2.0)))+T(1.0) );
}

template <class T>
T gain(T g, T x) {
    return (x<T(0.5))
    ?T(0.5)*bias<T>(T(1.0)-g,T(2.0)*x)
    :T(1.0)-bias<T>(T(1.0)-g,T(2.0)-T(2.0)*x)*T(0.5);
}

template <class T>
T sgain(T g, T x) {
    T t = (T(1.0)-T(2.0)*x)*((T(1.0)/g)-T(2.0));
    return (x<T(0.5))
    ?   x *T(1.0)/( t+T(1.0))
    :(t-x)*T(1.0)/( t-T(1.0));
}

//TODO (types)
/*template <class T>
T sphong(T n, T x) {
S (t) := t / (n-nt+t)
 n
}*/

};
#endif

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