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@jcponce
jcponce committed Mar 29, 2024
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44 changes: 22 additions & 22 deletions function-plotter/README.md
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Expand Up @@ -49,37 +49,37 @@ You can also visualize complex functions plotted with the domain coloring method

#### Examples

* [z * (1-z)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=z*(1-z))
* [1/z + i * z^(1/2)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=1/z+i*z^(1/2))
* [z + pi * log(z + e)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=z+pi*log(z+e))
* [e^z + t](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=e^z+t)
* [z * (1-z)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=eiAqICgxLXop)
* [1/z + i * z^(1/2)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=MS96K2kqel4oMS8yKQ==)
* [z + pi * log(z + e)](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=eiArIHBpICogbG9nKHogKyBlKQ==)
* [e^z + t](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=ZV56ICsgdA==)
* [s * i + s - 0.09 * (z - 6)^2](https://www.dynamicmath.xyz/complex/function-plotter/index.htm?expression=s*i+s-0.09*(z-6)^2)
* [sin(z + pi)/tanh(z^2 - i) + t](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=sin(z+pi)/tanh(z^2-i)+t)
* [sin(z + pi)/tanh(z^2 - i) + t](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=cyAqIGkgKyBzIC0gMC4wOSAqICh6IC0gNileMg==)

## Some interesting examples about conformal mapping

* [Fluid around cylinder](https://www.dynamicmath.xyz/complex/function-plotter/?expression=z*(1-(t+1)/2)+(t+1)/2*(z+1/z))
* [Real component](https://www.dynamicmath.xyz/complex/function-plotter/?expression=re((z+1/z))*(t+1)/2+re(z)*(1-(t+1)/2))
* [Imaginary component](https://www.dynamicmath.xyz/complex/function-plotter/?expression=im((z+1/z))*(t+1)/2+im(z)*(1-(t+1)/2))
* [Disk with a rotating tile](https://www.dynamicmath.xyz/complex/function-plotter/?expression=(z*0.99+0.01*((1-z^(18))*z^2))*(1+i*t))
* [Bending reality](https://www.dynamicmath.xyz/complex/function-plotter/?expression=e^(i*0.5*(z-3*i)+log(z-3*i))*(t+1)/2+z*(1-(t+1)/2))
* [Vortex within a circle](https://www.dynamicmath.xyz/complex/function-plotter/?expression=(z*3)/2*e^(t*pi*i*e^(-1*abs((z*3)/2)^2)))
* [Waves](https://www.dynamicmath.xyz/complex/function-plotter/?expression=e^(i*(1.5*r)^5)+t)
* [Potential](https://www.dynamicmath.xyz/complex/function-plotter/?expression=(log((z-1)/(z+1)))*(t+1)/2+z*(1-(t+1)/2))
* [Transform the unit circle to the UHP](https://www.dynamicmath.xyz/complex/function-plotter/?expression=transform(z,(z-i)/(z+i),t)*disk(transform(z,(z-i)/(z+i),t)))
* [Joukowsky airfoil](https://www.dynamicmath.xyz/complex/function-plotter/?expression=joukowsky(z,-0.15+0.23*i,1.17))
* [Loxodromic](https://www.dynamicmath.xyz/complex/function-plotter/?expression=((0.255+0.763*i)*log((z-1)/(z+1)))+s)
* [Fluid around cylinder](https://www.dynamicmath.xyz/complex/function-plotter/?expression=eiooMS0odCsxKS8yKSsodCsxKS8yKih6KzEveik=)
* [Real component](https://www.dynamicmath.xyz/complex/function-plotter/?expression=cmUoKHorMS96KSkqKHQrMSkvMityZSh6KSooMS0odCsxKS8yKQ==)
* [Imaginary component](https://www.dynamicmath.xyz/complex/function-plotter/?expression=aW0oKHorMS96KSkqKHQrMSkvMitpbSh6KSooMS0odCsxKS8yKQ==)
* [Disk with a rotating tile](https://www.dynamicmath.xyz/complex/function-plotter/?expression=KHoqMC45OSswLjAxKigoMS16XigxOCkpKnpeMikpKigxK2kqdCk=)
* [Bending reality](https://www.dynamicmath.xyz/complex/function-plotter/?expression=ZV4oaSowLjUqKHotMyppKStsb2coei0zKmkpKSoodCsxKS8yK3oqKDEtKHQrMSkvMik=)
* [Vortex within a circle](https://www.dynamicmath.xyz/complex/function-plotter/?expression=KHoqMykvMiplXih0KnBpKmkqZV4oLTEqYWJzKCh6KjMpLzIpXjIpKQ==)
* [Waves](https://www.dynamicmath.xyz/complex/function-plotter/?expression=ZV4oaSooMS41KnIpXjUpK3Q=)
* [Potential](https://www.dynamicmath.xyz/complex/function-plotter/?expression=KGxvZygoei0xKS8oeisxKSkpKih0KzEpLzIreiooMS0odCsxKS8yKQ==)
* [Transform the unit circle to the UHP](https://www.dynamicmath.xyz/complex/function-plotter/?expression=dHJhbnNmb3JtKHosKHotaSkvKHoraSksdCkqZGlzayh0cmFuc2Zvcm0oeiwoei1pKS8oeitpKSx0KSk=)
* [Joukowsky airfoil](https://www.dynamicmath.xyz/complex/function-plotter/?expression=am91a293c2t5KHosLTAuMTUrMC4yMyppLDEuMTcp)
* [Loxodromic](https://www.dynamicmath.xyz/complex/function-plotter/?expression=KCgwLjI1NSswLjc2MyppKSpsb2coKHotMSkvKHorMSkpKStz)

## Examples about domain coloring

* Analytic functions:
* [sin(z + t)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=sin(z+t))
* [z * t + 1/sin(z)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=z*t+1/sin(z))
* [z^(10 * (t + 1)/2 + 2) - 1](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=z^(10*(t+1)/2+2)-1)
* [(z-1)/(z^2+z+1) * (t+1)/2 + z * ( 1- (t+1)/2 )](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=(z-1)/(z^2+z+1)*(t+1)/2+z*(1-(t+1)/2))
* [sin(z + t)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=c2luKHordCk=)
* [z * t + 1/sin(z)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=eip0KzEvc2luKHop)
* [z^(10 * (t + 1)/2 + 2) - 1](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=el4oMTAqKHQrMSkvMisyKS0x)
* [(z-1)/(z^2+z+1) * (t+1)/2 + z * ( 1- (t+1)/2 )](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=KHotMSkvKHpeMit6KzEpKih0KzEpLzIreiooMS0odCsxKS8yKQ==)
* Non-Analytic functions:
* [(z+1) * conj(z)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=(z+1)*conj(z))
* [conj(z) * (t+1)/2 + cos(z * ( 1- (t+1)/2 ))](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=conj(z)*(t+1)/2+cos(z*(1-(t+1)/2)))
* [(z+1) * conj(z)](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=KHorMSkqY29uaih6KQ==)
* [conj(z) * (t+1)/2 + cos(z * ( 1- (t+1)/2 ))](https://www.dynamicmath.xyz/complex/function-plotter/hsv.htm?expression=Y29uaih6KSoodCsxKS8yK2Nvcyh6KigxLSh0KzEpLzIpKQ==)


## How does it work?
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48 changes: 26 additions & 22 deletions function-plotter/scripts/main.js
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Expand Up @@ -230,35 +230,39 @@ $('#texture-options a').each(function () {

// When the user presses the button, show some copyable text
function showLink() {
//let expression_base64 = encodeURI($("#equation-input").val());
let expression_unicode = encodeURI($("#equation-input").val());

let url = [location.protocol, "//", location.host, location.pathname].join(
""
);
url = url + "?expression=" + (expression_unicode);
//url = url + "?expression=" + expression_base64;

$("#copyable-link").val(url);
$("#link-container").show();
$("#copyable-link").select();
const expressionBase64 = btoa($('#equation-input').val());
let url = `${location.protocol}//${location.host}${location.pathname}?expression=${expressionBase64}`;
$('#copyable-link').val(url);
$('#link-container').show();
$('#copyable-link').select();
}
$("#copyable-link").blur(function () {
$("#link-container").hide();

// Hide the link container when the copyable link loses focus
$('#copyable-link').blur(function () {
$('#link-container').hide();
});

// If the user already specified
// Check if the user already specified an expression in the URL
$(function () {
//var expression_base64 = getQueryVariable("expression");
var expression_unicode = getQueryVariable("expression");
//console.log(expression_base64);
//if (expression_base64) {
if (expression_unicode) {
//$("#equation-input").val(atob(expression_base64.replace("/", "")));
$("#equation-input").val(decodeURIComponent(expression_unicode));
const expressionBase64 = getQueryVariable('expression');
if (expressionBase64) {
$('#equation-input').val(atob(expressionBase64.replace('/', '')));
}
});

// Function to get the value of a query variable from the URL
function getQueryVariable(variable) {
const query = window.location.search.substring(1);
const vars = query.split('&');
for (let i = 0; i < vars.length; i++) {
const pair = vars[i].split('=');
if (decodeURIComponent(pair[0]) === variable) {
return decodeURIComponent(pair[1]);
}
}
return null;
}

// Get things started.
$('#equation-input').change(update_expression);
$('#show-link').click(showLink);
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48 changes: 26 additions & 22 deletions function-plotter/scripts/mainhsv.js
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Original file line number Diff line number Diff line change
Expand Up @@ -275,35 +275,39 @@ $("#texture-options a").each(function () {

// When the user presses the button, show some copyable text
function showLink() {
//let expression_base64 = btoa($("#equation-input").val());
let expression_unicode = encodeURI($("#equation-input").val());

let url = [location.protocol, "//", location.host, location.pathname].join(
""
);
url = url + "?expression=" + expression_unicode;
//url = url + "?expression=" + expression_base64;

$("#copyable-link").val(url);
$("#link-container").show();
$("#copyable-link").select();
const expressionBase64 = btoa($('#equation-input').val());
let url = `${location.protocol}//${location.host}${location.pathname}?expression=${expressionBase64}`;
$('#copyable-link').val(url);
$('#link-container').show();
$('#copyable-link').select();
}
$("#copyable-link").blur(function () {
$("#link-container").hide();

// Hide the link container when the copyable link loses focus
$('#copyable-link').blur(function () {
$('#link-container').hide();
});

// If the user already specified
// Check if the user already specified an expression in the URL
$(function () {
//var expression_base64 = getQueryVariable("expression");
var expression_unicode = getQueryVariable("expression");
//console.log(expression_base64);
//if (expression_base64) {
if (expression_unicode) {
//$("#equation-input").val(atob(expression_base64.replace("/", "")));
$("#equation-input").val(decodeURIComponent(expression_unicode));
const expressionBase64 = getQueryVariable('expression');
if (expressionBase64) {
$('#equation-input').val(atob(expressionBase64.replace('/', '')));
}
});

// Function to get the value of a query variable from the URL
function getQueryVariable(variable) {
const query = window.location.search.substring(1);
const vars = query.split('&');
for (let i = 0; i < vars.length; i++) {
const pair = vars[i].split('=');
if (decodeURIComponent(pair[0]) === variable) {
return decodeURIComponent(pair[1]);
}
}
return null;
}

// Get things started.
$("#equation-input").change(update_expression);
$("#show-link").click(showLink);
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