I'm creating an visual EQ using the Web Audio API and canvas. I am plotting frequencies in a logarithmic graph on a HTML5 Canvas using the following function:
function frequencyToPixel(freq){
var min = Math.log(graph.min)/Math.log(10)
, max = Math.log(graph.max)/Math.log(10)
, range = max-min
, pixel = (Math.log(freq)/Math.log(10) - min) / range * canvas.width;
return pixel;
}
I would like to also reverse this equation to get a function that returns the frequency that a particular pixel relates to. At the moment I'm using the following function but it's not producing the desired result. For example if I input 1000 into the above function it returns 434.93. I should therefore be able to put 434.93 into the below equation to return 1000;
function pixelToFrequency(pixel){
var min = Math.log(graph.min)/Math.log(10)
, max = Math.log(graph.max)/Math.log(10)
, range = max-min
, x = (pixel * canvas.width * range) + min
, frequency = Math.pow(10, x);
return frequency;
}
It's likely i've rearranged the equation in the wrong way so any help would be much appreciated.
The function below works out the frequency for a given pixel on the logarithmic-scaled canvas frequency graph:
function pixelToFrequency(pixel){
var min = Math.log(app.graph.min)/Math.log(10)
, max = Math.log(app.graph.max)/Math.log(10)
, range = max-min
, frequency = Math.pow(10, pixel * (range / canvas.width) + min)
return frequency;
}
pixel = (Math.log(freq)/Math.log(10) - min) / range * canvas.width
Try this?
freq = E((Math.log(10) * (pixel * (range / canvas.width)))+ Math.log(graph.min))
See if that helps at all. Where E is the Euler's Number raised to the parameters in parenthesis. It might be equivalent to what you have there, I didn't look to closely too be honest. It's worth a shot though.
Related
I'm trying to calculate the volume of a sphere, with floating points, but I couldn't quite understand the logic behind the exercise.
Write a program that calculates and displays the volume of a sphere,
providing the value of its radius (R). The formula for calculating
volume is: (4/3) * pi * R3. Consider (assign) to pi the value 3.14159.
const PI = 3.14159;
let R = parseFloat(gets());
//TODO: Fill in the blanks with a possible solution to the challenge
print("VOLUME = " + );
You should try by yourself, but here is the solution and explanation.
If you are using javascript on the browser:
let radius = parseFloat(prompt("Enter value for radius: "));
let volume = 4/3 * Math.PI * Math.pow(radius, 3);
console.log("The volume is: ", volume);
We are requesting the user input with prompt() and assigning it to radius variable. We calculate the volume with the equation v = 4/3 πr³, Math.PI represents the number PI and Math.pow() calculates the given base (this case, radius) taken to the power of the given exponent. Last step is to print the result to the output, which is done with console.log()
Reading a lot of the tips here, I solved it, I don't know if it's the best way, but I solved it.
const PI = 3.14159;
let R = parseFloat(gets());
var raio = parseFloat(R);
var volumeEsfera = (4/3) * PI * Math.pow(raio, 3);
print("VOLUME = " + volumeEsfera.toFixed(3) );
After I saw a video from the Coding Train on youtube about fractal trees, I tried to build one myself. Which worked great and I played with some variables to get different results.
I would love to see the tree moving like it got hit by some wind. I tried different approaches like rotating the branches a little bit or some minor physics implementations but that failed miserably.
So my question is: What would be the best approach to render a fractal tree and give it some sort of "life" like little shakes from wind.
Is there some sort of good reference ?
Do I need physics ? -> If so where do I have to look ?
If not -> How could I fake such an effect?
I am glad about every help I can get.
Source for the idea: https://www.youtube.com/watch?v=0jjeOYMjmDU
Tree in the wind.
The following are some short points re bending a branch in the wind. As the whole solution is complex you will have to get what you can from the code.
The code includes a seeded random number functions. A random recursive tree renderer, a poor quality random wind generator, all drawn on canvas using an animation loop.
Wind
To apply wind you need to add a bending force to each branch that is proportional to the angle of the branch to the wind.
So if you have a branch in direction dir and a wind in the direct wDir the amount of scaling the bending force needs is
var x = Math.cos(dir); // get normalize vector for the branch
var y = Math.sin(dir);
var wx = Math.cos(wDir); // get normalize vector for the wind
var wy = Math.sin(wDir);
var forceScale = x * wy - y * wx;
The length of the branch also effects the amount of force to include that you lengthen the vector of the branch to be proportional to its length
var x = Math.cos(dir) * length; // get normalize vector for the branch
var y = Math.sin(dir) * length;
var wx = Math.cos(wDir); // get normalize vector for the wind
var wy = Math.sin(wDir);
var forceScale = x * wy - y * wx;
Using this method ensures that the branches do not bend into the wind.
There is also the thickness of the branch, this is a polynomial relationship related to the cross sectional area. This is unknown so is scaled to the max thickness of the tree (an approximation that assumes the tree base can not bend, but the end branches can bend a lot.)
Then the elastic force of the bent branch will have a force that moves the branch back to its normal position. This acts like a spring and is very much the same as the wind force. As the computational and memory load would start to overwhelm the CPU we can cheat and use the wind to also recoil with a little bit of springiness.
And the tree.
The tree needs to be random, yet being fractal you don't want to store each branch. So you will also need a seeded random generator that can be reset at the start of each rendering pass. The tree is rendered randomly with each iteration but because the random numbers start at the same seed each time you get the same tree.
The example
Draws random tree and wind in gusts. Wind is random so tree may not move right away.
Click tree image to reseed the random seed value for the tree.
I did not watch the video, but these things are quite standard so the recursive function should not be to far removed from what you may have. I did see the youTube cover image and it looked like the tree had no randomness. To remove randomness set the leng, ang, width min, max to be the same. eg angMin = angMax = 0.4; will remove random branch angles.
The wind strength will max out to cyclone strength (hurricane for those in the US) to see the max effect.
There are a zillion magic numbers the most important are as constants with comments.
const ctx = canvas.getContext("2d");
// click function to reseed random tree
canvas.addEventListener("click",()=> {
treeSeed = Math.random() * 10000 | 0;
treeGrow = 0.1; // regrow tree
});
/* Seeded random functions
randSeed(int) int is a seed value
randSI() random integer 0 or 1
randSI(max) random integer from 0 <= random < max
randSI(min, max) random integer from min <= random < max
randS() like Math.random
randS(max) random float 0 <= random < max
randS(min, max) random float min <= random < max
*/
const seededRandom = (() => {
var seed = 1;
return { max : 2576436549074795, reseed (s) { seed = s }, random () { return seed = ((8765432352450986 * seed) + 8507698654323524) % this.max }}
})();
const randSeed = (seed) => seededRandom.reseed(seed|0);
const randSI = (min = 2, max = min + (min = 0)) => (seededRandom.random() % (max - min)) + min;
const randS = (min = 1, max = min + (min = 0)) => (seededRandom.random() / seededRandom.max) * (max - min) + min;
/* TREE CONSTANTS all angles in radians and lengths/widths are in pixels */
const angMin = 0.01; // branching angle min and max
const angMax= 0.6;
const lengMin = 0.8; // length reduction per branch min and max
const lengMax = 0.9;
const widthMin = 0.6; // width reduction per branch min max
const widthMax = 0.8;
const trunkMin = 6; // trunk base width ,min and max
const trunkMax = 10;
const maxBranches = 200; // max number of branches
const windX = -1; // wind direction vector
const windY = 0;
const bendability = 8; // greater than 1. The bigger this number the more the thin branches will bend first
// the canvas height you are scaling up or down to a different sized canvas
const windStrength = 0.01 * bendability * ((200 ** 2) / (canvas.height ** 2)); // wind strength
// The wind is used to simulate branch spring back the following
// two number control that. Note that the sum on the two following should
// be below 1 or the function will oscillate out of control
const windBendRectSpeed = 0.01; // how fast the tree reacts to the wing
const windBranchSpring = 0.98; // the amount and speed of the branch spring back
const gustProbability = 1/100; // how often there is a gust of wind
// Values trying to have a gusty wind effect
var windCycle = 0;
var windCycleGust = 0;
var windCycleGustTime = 0;
var currentWind = 0;
var windFollow = 0;
var windActual = 0;
// The seed value for the tree
var treeSeed = Math.random() * 10000 | 0;
// Vars to build tree with
var branchCount = 0;
var maxTrunk = 0;
var treeGrow = 0.01; // this value should not be zero
// Starts a new tree
function drawTree(seed) {
branchCount = 0;
treeGrow += 0.02;
randSeed(seed);
maxTrunk = randSI(trunkMin, trunkMax);
drawBranch(canvas.width / 2, canvas.height, -Math.PI / 2, canvas.height / 5, maxTrunk);
}
// Recusive tree
function drawBranch(x, y, dir, leng, width) {
branchCount ++;
const treeGrowVal = (treeGrow > 1 ? 1 : treeGrow < 0.1 ? 0.1 : treeGrow) ** 2 ;
// get wind bending force and turn branch direction
const xx = Math.cos(dir) * leng * treeGrowVal;
const yy = Math.sin(dir) * leng * treeGrowVal;
const windSideWayForce = windX * yy - windY * xx;
// change direction by addition based on the wind and scale to
// (windStrength * windActual) the wind force
// ((1 - width / maxTrunk) ** bendability) the amount of bending due to branch thickness
// windSideWayForce the force depending on the branch angle to the wind
dir += (windStrength * windActual) * ((1 - width / maxTrunk) ** bendability) * windSideWayForce;
// draw the branch
ctx.lineWidth = width;
ctx.beginPath();
ctx.lineTo(x, y);
x += Math.cos(dir) * leng * treeGrowVal;
y += Math.sin(dir) * leng * treeGrowVal;
ctx.lineTo(x, y);
ctx.stroke();
// if not to thing, not to short and not to many
if (branchCount < maxBranches && leng > 5 && width > 1) {
// to stop recusive bias (due to branch count limit)
// random select direction of first recusive bend
const rDir = randSI() ? -1 : 1;
treeGrow -= 0.2;
drawBranch(
x,y,
dir + randS(angMin, angMax) * rDir,
leng * randS(lengMin, lengMax),
width * randS(widthMin, widthMax)
);
// bend next branch the other way
drawBranch(
x,y,
dir + randS(angMin, angMax) * -rDir,
leng * randS(lengMin, lengMax),
width * randS(widthMin, widthMax)
);
treeGrow += 0.2;
}
}
// Dont ask this is a quick try at wind gusts
// Wind needs a spacial component this sim does not include that.
function updateWind() {
if (Math.random() < gustProbability) {
windCycleGustTime = (Math.random() * 10 + 1) | 0;
}
if (windCycleGustTime > 0) {
windCycleGustTime --;
windCycleGust += windCycleGustTime/20
} else {
windCycleGust *= 0.99;
}
windCycle += windCycleGust;
currentWind = (Math.sin(windCycle/40) * 0.6 + 0.4) ** 2;
currentWind = currentWind < 0 ? 0 : currentWind;
windFollow += (currentWind - windActual) * windBendRectSpeed;
windFollow *= windBranchSpring ;
windActual += windFollow;
}
requestAnimationFrame(update);
function update() {
ctx.clearRect(0,0,canvas.width,canvas.height);
updateWind();
drawTree(treeSeed);
requestAnimationFrame(update);
}
body {
font-family : arial;
}
<canvas id="canvas" width="250" heigth="200"></canvas>
Click tree to reseed.
Update
I just noticed that the wind and branch length are absolute thus drawing the tree on a larger canvas will create a bending force too great and the branches will bend past the wind vector.
To scale the sim up either do it via a global scale transform, or reduce the windStrength constant to some smaller value. You will have to play with the value as its a 2nd order polynomial relation. My guess is multiply it with (200 ** 2) / (canvas.height ** 2) where the 200 is the size of the example canvas and the canvas.height is the new canvas size.
I have added the calculations to the example, but its not perfect so when you scale you will have to change the value windStrength (the first number) down or up if the bending is too far or not enough.
I am aware that random integers can be generated in JavaScript like this:
function getRandomInt(min, max) {
return Math.floor(Math.random() * (max - min + 1)) + min;
}
But what I want is a set of random numbers that are biased towards a specific value.
As an example, if my specific center value is 200, I want a set of random numbers that has a large range, but mostly around 200. Hopefully there will be a function like
biasedRandom(center, biasedness)
It sounds like a Gaussian distribution might be about right here.
This stackoverflow post describes how to produce something that is Gaussian in shape. We can then scale and shift the distribution by two factors;
The mean (200 in this case) which is where the distribution is centred
The variance which gives control over the width of the distribution
I have included a histogram of the generated numbers (using plotly) in my example so you can easily see how varying these two parameters v and mean affects the numbers generated. In your real code you would not need to include the plotly library.
// Standard Normal variate using Box-Muller transform.
function randn_bm() {
var u = 0, v = 0;
while(u === 0) u = Math.random(); //Converting [0,1) to (0,1)
while(v === 0) v = Math.random();
return Math.sqrt( -2.0 * Math.log( u ) ) * Math.cos( 2.0 * Math.PI * v );
}
//generate array
// number of points
let n = 50;
// variance factor
let v = 1;
// mean
let mean = 200;
let numbers = []
for (let i=0; i<n;i++){
numbers.push(randn_bm())
}
// scale and shift
numbers = numbers.map( function (number){ return number*v + mean})
// THIS PURELY FOR PLOTTING
var trace = {
x: numbers,
type: 'histogram',
};
var data = [trace];
Plotly.newPlot('myDiv', data);
<script src="https://cdn.plot.ly/plotly-latest.min.js"></script>
<div id="myDiv"></div>
I am trying to write a function that calculates the soft light given a foreground and a background color.
The function is below;
var background = '0xFFFFFF';
var foreground = '0x47768C';
var calculateSoftlight = function (background, foreground) {
var intBackground = parseInt(background, 16);
var intForeground = parseInt(foreground, 16);
var softlight = (1 - (2 * intForeground)) * (intBackground*intBackground) + (2 * intForeground * intBackground);
return softlight.toString(16);
}
calculateSoftlight(background, foreground); //-8eed155338bb200000
I am using the Pegtop formula as listed here; http://en.wikipedia.org/wiki/Blend_modes. I am unsure of the correct implementation of this. Any ideas?
Apply the formula to each RGB value instead of using Hex. If you need to use Hex as an input you'll probably need to convert.
You will need to normalize each value (so value / 255) and use that in the formula. Then multiply (and round) the result by 255 to convert back to 8-bit value.
Something like this should be close, I haven't used that formula specifically though so this is untested.
var top = top / 255,
bot = bot / 255;
top = ((1 - 2*bot)*Math.pow(top, 2)) + 2*bot*top,
top = Math.round(top * 255);
I'm trying to find an algorithm for generating a Y axis for a chart engine I'm writing and am at the pulling out hair stage.
Searching around yields various solutions however I'm struggling to find one that caters for all data ranges.
Here's what I've got so far:
// Raise the max and lower the min so that we get a prettier looking chart.
var tickRangeMinMax = maxValue - minValue;
var min = tickRangeMinMax * Math.round(minValue / tickRangeMinMax);
var max = tickRangeMinMax * Math.round(1 + (maxValue / tickRangeMinMax));
This gives me a new range for which I'd like to generate a Y axis.
I calculate the distance between each YAxis label as follows:
var ticks = tickRange(min, max, labelCount);
function tickRange(minVal, maxVal, tickCount) {
var range = maxVal - minVal;
var unRoundedTicksSize = range / (tickCount - 1);
var x = Math.ceil(log10(unRoundedTicksSize) - 1);
var pow10X = Math.pow(10, x);
var roundedTickRange = Math.ceil(unRoundedTicksSize / pow10X) * pow10X;
return roundedTickRange;
}
I've also tried calculating the ticks using the much simpler algorithm:
return (max - min) / labelCount
The former method works well with small ranges such as 23 -> 200 however neither of these methods work well for me when I've got a range of say, 0 -> 3000.
In the case of 0 -> 3000 I end up with negative values in some of my labels.
I add labels to the label collection by looping over the labelCount, in my case it's 5, and subtracting the tick range from the previous label value. I start with the max value.
For reference, same as yours only in Python (don't speak JS):
import math
def ticks (low, high, labels):
nlabels = len(labels)
tick = (high - low) / (nlabels - 1)
x = math.floor(math.log10(tick))
pow10x = math.pow(10,x)
tick = int(math.ceil(tick/pow10x)*pow10x)
return zip (range(low,high+tick,tick), labels)
print (ticks (0, 225, ['a', 'b', 'c', 'd', 'e']))
PS. maybe floor on the logarithm is better