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adammaj1 / Waveform

Waveform or data types

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cgccwaveformwaveform-datawaveform-generatorwaveforms1dgraygreygreyscale

Description

Names or nomenclature comparison

All functions work in the range [0..1].

Algorithm:

  • take input function f which maps floating point number (x or position) in a normalised range [0.0, 1.0] and gives monotone output ( A monotonically non-decreasing function )
  • make function diagram and color gradient ( image of continous color gradient) using above function
  • make 3 types of periodic waves for each function type using ModifyPosition function
  • make color diagram and color gradient for each GradientJoiningType of input function
typedef enum  {no, steps, tubes } GradientJoiningType; 



double ModifyPosition(const double position, const GradientJoiningType GradientJoining){
	
	// input position  should be in  [0,1] range 
	double p = position; // p = local copy of position
	// if position > 1 then we have repetition of colors = periodic function = wave   
	
	
	switch(GradientJoining){
	
		case no : {break;} // return input position witout modifications
		
		// periodic waves with different joinings
		case steps : {	p = p * segments; // periodic  = change range
				p = frac(p); 
    				break;}
    				
		case tubes : {	p = p * segments; // periodic = change range
				int ip = (int)p;
      				p = p-ip; // fractional part 
      				if (ip % 2) {p = 1.0-p;} // reverse gradient
				break;}
		default:{}
	}
	
	return p; // output in [0,1] range

}

So important variables:

  • coordinate ( integer to float)
  • position ( float )
  • color (RGB) : float to integer in [0 , 255] range

old images ( made using ./src/d/d.c)

Linear function graph = made using continous_data function

Step function graph. Made using discrete_data function

Sawtooth wave graph. Made using sawtooth_data function which includes steps type of joining

Sine wave

Piecewise linear functions: Boxcar function or square waveform or Rectangular function, the simplest step_function. It is made using square_wave function

Triangle wave = made from linear function using tubes type of joining

new images ( made using ./src/g/g.c)

Linear Linear_no

Linear_steps

Linear_tubes

Quadratic Quadratic_no

Quadratic_steps

Quadratic_tubes

Cubic Cubic_no

Cubic_steps

Cubic_tubes

CubicInv CubicInv_no

CubicInv_steps

CubicInv_tubes

Sqrt Sqrt_no

Sqrt_steps

Sqrt_tubes

Root Root_no

Root_steps

Root_tubes

Gamma Gamma_no

Gamma_steps

Gamma_tubes

LSin LSin_no

effect of a sine wave superimposed on a ramp function

It is based on the The Colour Map Test Image by Peter Kovesi

LSin_steps

LSin_tubes

SinExp SinExp_no

SinExp_steps

SinExp_tubes

Sin Sin_no

Sin_steps

Sin_tubes

Smooth Smooth_no

Smooth_steps

Smooth_tubes

Tanh Tanh_no

Tanh_steps

Tanh_tubes

smoothstep_Cubic_Polynomial smoothstep_Cubic_Polynomial_no

smoothstep_Cubic_Polynomial_steps

smoothstep_Cubic_Polynomial_tubes

inv_smoothstep_Cubic_Polynomial inv_smoothstep_Cubic_Polynomial_no

inv_smoothstep_Cubic_Polynomial_steps

inv_smoothstep_Cubic_Polynomial_tubes

smoothstep_Quartic_Polynomial smoothstep_Quartic_Polynomial_no

smoothstep_Quartic_Polynomial_steps

smoothstep_Quartic_Polynomial_tubes

inv_smoothstep_Quartic_Polynomial inv_smoothstep_Quartic_Polynomial_no

inv_smoothstep_Quartic_Polynomial_steps

inv_smoothstep_Quartic_Polynomial_tubes

smoothstep_Quintic_Polynomial smoothstep_Quintic_Polynomial_no

smoothstep_Quintic_Polynomial_steps

smoothstep_Quintic_Polynomial_tubes

smoothstep_Quadratic_Rational smoothstep_Quadratic_Rational_no

smoothstep_Quadratic_Rational_steps

smoothstep_Quadratic_Rational_tubes

inv_smoothstep_Quadratic_Rational inv_smoothstep_Quadratic_Rational_no

inv_smoothstep_Quadratic_Rational_steps

inv_smoothstep_Quadratic_Rational_tubes

smoothstep_Cubic_Rational smoothstep_Cubic_Rational_no

smoothstep_Cubic_Rational_steps

smoothstep_Cubic_Rational_tubes

inv_smoothstep_Cubic_Rational inv_smoothstep_Cubic_Rational_no

inv_smoothstep_Cubic_Rational_steps

inv_smoothstep_Cubic_Rational_tubes

smoothstep_Rational smoothstep_Rational_no

smoothstep_Rational_steps

smoothstep_Rational_tubes

inv_smoothstep_Rational inv_smoothstep_Rational_no

inv_smoothstep_Rational_steps

inv_smoothstep_Rational_tubes

smoothstep_Piecewise_Quadratic smoothstep_Piecewise_Quadratic_no

smoothstep_Piecewise_Quadratic_steps

smoothstep_Piecewise_Quadratic_tubes

inv_smoothstep_Piecewise_Quadratic inv_smoothstep_Piecewise_Quadratic_no

inv_smoothstep_Piecewise_Quadratic_steps

inv_smoothstep_Piecewise_Quadratic_tubes

smoothstep_Piecewise_Polynomial smoothstep_Piecewise_Polynomial_no

smoothstep_Piecewise_Polynomial_steps

smoothstep_Piecewise_Polynomial_tubes

inv_smoothstep_Piecewise_Polynomial inv_smoothstep_Piecewise_Polynomial_no

inv_smoothstep_Piecewise_Polynomial_steps

inv_smoothstep_Piecewise_Polynomial_tubes

smoothstep_Trigonometric smoothstep_Trigonometric_no

smoothstep_Trigonometric_steps

smoothstep_Trigonometric_tubes

inv_smoothstep_Trigonometric inv_smoothstep_Trigonometric_no

inv_smoothstep_Trigonometric_steps

inv_smoothstep_Trigonometric_tubes

almostIdentity almostIdentity_no

almostIdentity_steps

almostIdentity_tubes

almostIdentity2 almostIdentity2_no

almostIdentity2_steps

almostIdentity2_tubes

almostUnitIdentity almostUnitIdentity_no

almostUnitIdentity_steps

almostUnitIdentity_tubes

integralSmoothstep integralSmoothstep_no

integralSmoothstep_steps

integralSmoothstep_tubes

expImpulse expImpulse_no

expImpulse_steps

expImpulse_tubes

quaImpulse quaImpulse_no

quaImpulse_steps

quaImpulse_tubes

polyImpulse polyImpulse_no

polyImpulse_steps

polyImpulse_tubes

expSustainedImpulse expSustainedImpulse_no

expSustainedImpulse_steps

expSustainedImpulse_tubes

cubicPulse cubicPulse_no

cubicPulse_steps

cubicPulse_tubes

expStep expStep_no

expStep_steps

expStep_tubes

gain gain_no

gain_steps

gain_tubes

parabola parabola_no

parabola_steps

parabola_tubes

pcurve pcurve_no

pcurve_steps

pcurve_tubes

sinc sinc_no

sinc_steps

sinc_tubes

trunc_fallof trunc_fallof_no

trunc_fallof_steps

trunc_fallof_tubes

source code

MWE

MRE = minimal reproducible ( working) example = short simple code

code in ./src/mwe/ directory

D directort

One file program that makes all images

Compile and run the program

gcc d.c -Wall -Wextra -lm
a.out > c.txt
gnuplot
plot "c.txt" with lines 
# save image as a c.png

G directory

code in ./src/g/ directory

One file program that makes all images. To run it:

make

FAQ

How to add new shaping function (transfer function or color function or mapping function) ?

  • add new functions named: Give_s
  • add new enum named: s in ColorTransferFunctionType
  • use s.c program to compute code for c functions (GiveRGB_Gray and GiveColor) and for gnuplot
  • copy code
// 
double Give_s(const double position){
	
	
  double s =  position;
  return s;
}

S directory contains c program for creating code for plot.gp and g.c

all curves in one image

curves by kynd.inf

Screen shot from online WebGL demo

available animation transition types: (the default transition type, 'linear', was omitted) from the wiki of the Sparrow Framework — the Open Source Game Engine for iOS.

online demos

Similar repo

Easing functions

by Iñigo Quilez

Smoothstep

Shaping functions

Polynomial Shaping Functions: This page presents a collection of polynomial functions for shaping, tweening, and easing signals in the range [0...1]. Functions include:

  • Blinn-Wyvill Approximation to the Raised Inverted Cosine
  • Double-Cubic Seat
  • Double-Cubic Seat with Linear Blend
  • Double-Odd-Polynomial Seat
  • Symmetric Double-Polynomial Sigmoids
  • Quadratic Through a Given Point

Exponential Shaping Functions

  • Exponential Ease-In and Ease-Out
  • Double-Exponential Seat
  • Double-Exponential Sigmoid
  • The Logistic Sigmoid

Circular & Elliptical Shaping Functions

  • Circular Interpolation: Ease-In and Ease-Out
  • Double-Circle Seat
  • Double-Circle Sigmoid
  • Double-Elliptic Seat
  • Double-Elliptic Sigmoid
  • Double-Linear with Circular Fillet
  • Circular Arc Through a Given Points

Bezier and Other Parametric Shaping Functions

  • Quadratic Bezier
  • Cubic Bezier
  • Cubic Bezier (Nearly) Through Two Given Points

List of interpolations

  • Linear Interpolation
  • Smooth Step
  • Smoother Step
  • Smoothest Step
  • Squared
  • Inverse Squared
  • Cubed
  • Sin
  • Catmull-Rom
  • Elastic In
  • Elastic Out
  • Wobble
  • Gaussian

Inspiration

This work is a spiritual descendent (not to say derivative work) of works done by the following individuals:

Dictionary

  • lerp = linear interpolation
  • Easing functions specify the rate of change of a parameter over time.
  • Exponential decay
  • Exponential growth: Exponential growth is the inverse of logarithmic growth
  • Logarithmic growth: Logarithmic growth is the inverse of exponential growth and is very slow
  • linear growth ( linear function): y = f(x) ; proportional or directly proportional if their corresponding elements have a constant ratio
  • Quadratic_growth
  • Hyperbolic_growth: If the output of a function is inversely proportional to its input, or inversely proportional to the difference from a given value x0, the function will exhibit hyperbolic growth, with a singularity at x0
  • Big O notation, see Orders of common functions

Git

git add README.md
git commit -m "first commit"
git branch -M main
git remote add origin git@github.com:adammaj1/Waveform.git
git push -u origin main

Subdirectory

mkdir images
git add *.png
git mv  *.png ./png
git commit -m "move"
git push -u origin main

then link the images:

![](./png/n.png "description of n.png image")

to overwrite

git mv -f

local repo :

~/Dokumenty/c/Waveform

License

File LICENSE must be in main repo directory to be read by github

Github

Math equation inside README.md

  • $\sqrt{3x-1}+(1+x)^2$

About

Waveform or data types

cgccwaveformwaveform-datawaveform-generatorwaveforms1dgraygreygreyscale

License:GNU General Public License v3.0

Languages

Language:C 96.9%Language:Gnuplot 2.4%Language:Shell 0.6%Language:Makefile 0.0%