d3.geo buffer around a feature - d3.js

Is it possible to draw a buffer (another feature) around a geographic feature in d3.js as a fixed distance unit (kilometers or miles)?
For instance, how would I draw a path around a point that extends 25 miles from that point in every direction. I've tried using d3.geo.circle and passing a fraction of degree (25 miles / approximately 69 miles per latitudinal degree or 25 / 69) but realize that although d3.geo.circle handles the reprojection of degrees, it does not accommodate for the differing lengths of each longitudinal degrees.
buffer = d3.geo.circle().angle(25/69).origin(function(x, y) { return [x, y]; })
I'm borrowing from this:
http://bl.ocks.org/mbostock/5628479
Update:
It looks like what I'd like to do is create a geodesic buffer.
Update:
I was able to create the buffer by drawing a path from a series of destination points given a distance and bearing from a start point.
See http://www.movable-type.co.uk/scripts/latlong.html for JavaScript implementation
Like this:
function drawBuffer(lat, long, distance){
var intervals = 18;
var intervalAngle = (360 / intervals);
var pointsData = [];
for(var i = 0; i < intervals; i++){
pointsData.push(getDestinationPoint(lat, long, i * intervalAngle, distance));
}
// Draw path using pointsData;
}

AFAIK doing this in D3 itself would be quite painful, as it's not really meant to create/modify features. I would recommend doing this as a preprocessing step in a GIS program such as QGIS, which allows you to buffer features in a number of ways. From there, you can export as GeoJSON and use with D3 in the usual way.

I was able to create a buffer around a point by drawing a path from a series of destination points given a distance and bearing from a start point.
See http://www.movable-type.co.uk/scripts/latlong.html for JavaScript implementation
Like this:
function drawBuffer(lat, long, distance){
var intervals = 18;
var intervalAngle = (360 / intervals);
var pointsData = [];
for(var i = 0; i < intervals; i++){
pointsData.push(getDestinationPoint(lat, long, i * intervalAngle, distance)); // See link
}
// Draw path using pointsData;
}

Related

Shape appears to have less vertexes than shape data THREE.JS

I'm trying to create a smooth "wave" when the mouse moves over isometric logo shape.
I've created in in processing now I'm trying to recreate it in THREE.js
The shape acts strangely - the shape doesn't look as smooth when elevated compared to the processing sketch. If you look at the edges you can see segments that are not supposed to be there. I'm not sure what causes this.
Basically the shape is created through a loops that goes over 2 arrays:
for (var i = 0; i < xpos0.length; i++) {
shape.lineTo(xpos0[i], ypos0[i]);
}
Then it animates through another for loop that checks the distance between verteces[i].x and mouse location intersection with the ground
for (let p = 0; p < mesh.geometry.vertices.length; p=p+1) {
let delta = Math.abs(mesh.geometry.vertices[p].x - intersects[0].point.x);
mesh.geometry.vertices[p].z = bump2(-2, 2000, -1, 2, delta);
}
z value is calculated through this function:
function bump2(a,b,c,d,xval) {
xval = parseFloat(xval);
// console.log(typeof xval);
return Math.exp(a / (-xval * xval / b + c) + d) * -1;
}
https://codepen.io/NotYetDesignLab/pen/JjYaqRJ
How it looks on THREE.JS
notice how some segments appear "broken", like it's made of stiff parts instead of the many points that make up the segment in the array and give the illusion of "paper".
THIS IS HOW IT'S SUPPOSED TO LOOK: (Processing/java)
This has been done using Processing. Notice how the elevation of the edges is smooth and not broken.

In A-Frame/THREE.js, is there a method like the Camera.ScreenToWorldPoint() from Unity?

I know a method from Unity whichs is very useful to convert a screen position to a world position : https://docs.unity3d.com/ScriptReference/Camera.ScreenToWorldPoint.html
I've been looking for something similar in A-Frame/THREE.js, but I didn't find anything.
Is there an easy way to convert a screen position to a world position in a plane which is positioned a given distance from the camera ?
This is typically done using Raycaster. An equivalent function using three.js would be written like this:
function screenToWorldPoint(screenSpaceCoord, target = new THREE.Vector3()) {
// convert the screen-space coordinates to normalized device coordinates
// (x and y ranging from -1 to 1):
const ndc = new THREE.Vector2()
ndc.x = 2 * screenSpaceCoord.x / screenWidth - 1;
ndc.y = 2 * screenSpaceCoord.y / screenHeight - 1;
// `Raycaster` can be used to convert this into a ray:
const raycaster = new THREE.Raycaster();
raycaster.setFromCamera(ndc, camera);
// finally, apply the distance:
return raycaster.ray.at(screenSpaceCoord.z, target);
}
Note that coordinates in browsers are usually measured from the top/left corner with y pointing downwards. In that case, the NDC calculation should be:
ndc.y = 1 - 2 * screenSpaceCoord.y / screenHeight;
Another note: instead of using a set distance in screenSpaceCoord.z you could also let three.js compute an intersection with any Object in your scene. For that you can use raycaster.intersectObject() and get a precise depth for the point of intersection with that object. See the documentation and various examples linked here: https://threejs.org/docs/#api/core/Raycaster

D3 Donut chart projected to sphere/globe

I want to use d3 for the next task:
display rotating globe with donut chart in center of every country. It should be possible to interact with globe (select country, zoom, rotate).
Seems d3 provide an easy way to implement every part of it but I can not get donuts part working as I need.
There is an easy way draw donut chart with the help of d3.arc:
var arc = d3.arc();
var data = [3, 23, 17, 35, 4];
var radius = 15/scale;
var _arc = arc.innerRadius(radius - 7/scale)
.outerRadius(radius).context(donutsContext);
var pieData = pie(data);
for (var i = 0; i < pieData.length; i++) {
donutsContext.beginPath();
donutsContext.fillStyle = color(i);
_arc(pieData[i]);
}
by with code as it is donuts are displayed on a plane on top of the globe, like:
globe with donut
​
while I want them to be 'wrapped' around the globe
There is d3.geoCircle method that can be projected to globe correctly. I got 'ring' projected correctly to the globe with the help of two circles:
var circle = d3.geoCircle()
.center(centroid)
.radius(2);
var outerCircle = circle();
var circle = d3.geoCircle()
.center(centroid)
.radius(1);
var innerCircle = circle();
var interCircleCoordinates = [];
for (var i = innerCircle.coordinates[0].length - 1; i >= 0; i--) {
interCircleCoordinates.push(innerCircle.coordinates[0][i]);
}
outerCircle.coordinates.push(interCircleCoordinates);
​globe with rings
but I really need to get a donut.
The other way I tried is getting image from donuts and wrapping this image around globe with the help of pixels manipulation:
var image = new Image;
image.onload = onload;
image.src = img;
function onload() {
window.dx = image.width;
window.dy = image.height;
context.drawImage(image, 0, 0, dx, dy);
sourceData = context.getImageData(0, 0, dx, dy).data;
target = context.createImageData(width, height);
targetData = target.data;
for (var y = 0, i = -1; y < height; ++y) {
for (var x = 0; x < width; ++x) {
var p = projection.invert([x, y]), λ = p[0], φ = p[1];
if (λ > 180 || λ < -180 || φ > 90 || φ < -90) { i += 4; continue; }
var q = ((90 - φ) / 180 * dy | 0) * dx + ((180 + λ) / 360 * dx | 0) << 2;
var r = sourceData[q];
var g = sourceData[++q];
var b = sourceData[++q];
targetData[++i] = r;
targetData[++i] = g;
targetData[++i] = b;
targetData[++i] = 125;//
}
}
context.clearRect(0,0, width, height);
context.putImageData(target, 0, 0);
};
by this way I get extremely slow rotating and interaction with a globe for a globe size I need (1000px)
So my questions are:
Is there is some way to project donuts that are generated with the help of d3.arc to a sphere (globe, orthographic projection)?
Is there is some way to get a donut from geoCircle?
Maybe there is some other way to achieve my goal I do not see
There is one way that comes to mind to display donuts on a globe. The key challenge is that d3 doesn't project three dimensional objects very well - with one exception, geographic features. Consequently, an "easy" solution is to convert your pie charts into geographic features and project them with the rest of your features.
To do this you need to:
Use a pie/donut generator as you normally would
Go along the paths generated to get points approximating the pie shape.
Convert the points to long/lat points
Assemble those points into geojson
Project them onto the map.
The first point is easy enough, just make a pie chart with an inner radius.
Now you have to select each path and find points along its perimeter using path.getPointAtLength(), this will be dependent on path length, so path.getTotalLength() will be handy (and corners are important, so you might want to incorporate a little bit of complexity for these corner cases to ensure you get them)).
Once you have the points, you need the use of a second projection, azimuthal equidistant would be best. If the pie chart is centered on [0,0] in svg coordinate space, rotate the azimuthal (don't center), so that the centroid coordinate is located at [0,0] in svg space (you can use translates on the pies to position them, but it will just add extra steps). Take each point and run it through projection.invert() using the second projection. You will need to update the projection for each donut chart as each one will have a different geographic centroid.
Once you have lat long points, it's easy - you've already done it with the geo circle function - convert to geojson and project with the orthographic projection.
This approach gave me something like:
Notes: Depending on your data, it might be easiest to preprocess your data into geojson and store that as opposed to calculating the geojson each page load.
You are using canvas, while you don't need to actually use an svg, you need to still be able to access svg functions like getPointAtLength, you do not need to have an svg or display svg elements by using a custom element replicating a path :
document.createElementNS(d3.namespaces.svg, 'path');
Oh, and make sure the second projection's translate is set - the default is [480,250] for all (most?) d3 projections, that will throw things off if unaccounted for.

Storing motion vectors from calculated optical flow in a practical way which enables reconstruction of subsequent frames from initial keyframes

I am trying to store the motion detected from optical flow for frames in a video sequence and then use these stored motion vectors in order to predict the already known frames using just the first frame as a reference. I am currently using two processing sketches - the first sketch draws a motion vector for every pixel grid (each of width and height 10 pixels). This is done for every frame in the video sequence. The vector is only drawn in a grid if there is sufficient motion detected. The second sketch aims to reconstruct the video frames crudely from just the initial frame of the video sequence combined with information about the motion vectors got from the first sketch.
My approach so far is as follows: I am able to determine the size, position and direction of each motion vector drawn in the first sketch from four variables. By creating four arrays (two for the motion vector's x and y coordinate and another two for its length in the x and y direction), every time a motion vector is drawn I can append each of the four variables to the arrays mentioned above. This is done for each pixel grid throughout an entire frame where the vector is drawn and for each frame in the sequence - via for loops. Once the arrays are full, I can then save them to a text file as a list of strings. I then load these strings from the text file into the second sketch, along with the first frame of the video sequence. I load the strings into variables within a while loop in the draw function and convert them back into floats. I increment a variable by one each time the draw function is called - this moves on to the next frame (I used a specific number as a separator in my text-files which appears at the end of every frame - the loop searches for this number and then increments the variable by one, thus breaking the while loop and the draw function is called again for the subsequent frame). For each frame, I can draw 10 by 10 pixel boxes and move then by the parameters got from the text files in the first sketch. My problem is simply this: How do I draw the motion of a particular frame without letting what I've have blitted to the screen in the previous frame affect what will be drawn for the next frame. My only way of getting my 10 by 10 pixel box is by using the get() function which gets pixels that are already drawn to the screen.
Apologies for the length and complexity of my question. Any tips would be very much appreciated! I will add the code for the second sketch. I can also add the first sketch if required, but it's rather long and a lot of it is not my own. Here is the second sketch:
import processing.video.*;
Movie video;
PImage [] naturalMovie = new PImage [0];
String xlengths [];
String ylengths [];
String xpositions [];
String ypositions [];
int a = 0;
int c = 0;
int d = 0;
int p;
int gs = 10;
void setup(){
size(640, 480, JAVA2D);
xlengths = loadStrings("xlengths.txt");
ylengths = loadStrings("ylengths.txt");
xpositions = loadStrings("xpositions.txt");
ypositions = loadStrings("ypositions.txt");
video = new Movie(this, "sample1.mov");
video.play();
rectMode(CENTER);
}
void movieEvent(Movie m) {
m.read();
PImage f = createImage(m.width, m.height, ARGB);
f.set(0, 0, m);
f.resize(width, height);
naturalMovie = (PImage []) append(naturalMovie, f);
println("naturalMovie length: " + naturalMovie.length);
p = naturalMovie.length - 1;
}
void draw() {
if(naturalMovie.length >= p && p > 0){
if (c == 0){
image(naturalMovie[0], 0, 0);
}
d = c;
while (c == d && c < xlengths.length){
float u, v, x0, y0;
u = float(xlengths[a]);
v = float(ylengths[a]);
x0 = float(xpositions[a]);
y0 = float(ypositions[a]);
if (u != 1.0E-19){
//stroke(255,255,255);
//line(x0,y0,x0+u,y0+v);
PImage box;
box = get(int(x0-gs/2), int(y0 - gs/2), gs, gs);
image(box, x0-gs/2 +u, y0 - gs/2 +v, gs, gs);
if (a < xlengths.length - 1){
a += 1;
}
}
else if (u == 1.0E-19){
if (a < xlengths.length - 1){
c += 1;
a += 1;
}
}
}
}
}
Word to the wise: most people aren't going to read that wall of text. Try to "dumb down" your posts so they get to the details right away, without any extra information. You'll also be better off if you post an MCVE instead of only giving us half your code. Note that this does not mean posting your entire project. Instead, start over with a blank sketch and only create the most basic code required to show the problem. Don't include any of your movie logic, and hardcode as much as possible. We should be able to copy and paste your code onto our own machines to run it and see the problem.
All of that being said, I think I understand what you're asking.
How do I draw the motion of a particular frame without letting what I've have blitted to the screen in the previous frame affect what will be drawn for the next frame. My only way of getting my 10 by 10 pixel box is by using the get() function which gets pixels that are already drawn to the screen.
Separate your program into a view and a model. Right now you're using the screen (the view) to store all of your information, which is going to cause you headaches. Instead, store the state of your program into a set of variables (the model). For you, this might just be a bunch of PVector instances.
Let's say I have an ArrayList<PVector> that holds the current position of all of my vectors:
ArrayList<PVector> currentPositions = new ArrayList<PVector>();
void setup() {
size(500, 500);
for (int i = 0; i < 100; i++) {
currentPositions.add(new PVector(random(width), random(height)));
}
}
void draw(){
background(0);
for(PVector vector : currentPositions){
ellipse(vector.x, vector.y, 10, 10);
}
}
Notice that I'm just hardcoding their positions to be random. This is what your MCVE should do as well. And then in the draw() function, I'm simply drawing each vector. This is like drawing a single frame for you.
Now that we have that, we can create a nextFrame() function that moves the vectors based on the ArrayList (our model) and not what's drawn on the screen!
void nextFrame(){
for(PVector vector : currentPositions){
vector.x += random(-2, 2);
vector.y += random(-2, 2);
}
}
Again, I'm just hardcoding a random movement, but you would be reading these from your file. Then we just call the nextFrame() function as the last line in the draw() function:
If you're still having trouble, I highly recommend posting an MCVE similar to mine and posting a new question. Good luck.

What are some algorithms that will allow me to simulate planetary physics?

I'm interested in doing a "Solar System" simulator that will allow me to simulate the rotational and gravitational forces of planets and stars.
I'd like to be able to say, simulate our solar system, and simulate it across varying speeds (ie, watch Earth and other planets rotate around the sun across days, years, etc). I'd like to be able to add planets and change planets mass, etc, to see how it would effect the system.
Does anyone have any resources that would point me in the right direction for writing this sort of simulator?
Are there any existing physics engines which are designed for this purpose?
It's everything here and in general, everything that Jean Meeus has written.
You need to know and understand Newton's Law of Universal Gravitation and Kepler's Laws of Planetary Motion. These two are simple and I'm sure you've heard about them, if not studied them in high school. Finally, if you want your simulator to be as accurate as possible, you should familiarize yourself with the n-Body problem.
You should start out simple. Try making a Sun object and an Earth object that revolves around it. That should give you a very solid start and it's fairly easy to expand from there. A planet object would look something like:
Class Planet {
float x;
float y;
float z; // If you want to work in 3D
double velocity;
int mass;
}
Just remember that F = MA and the rest just just boring math :P
This is a great tutorial on N-body problems in general.
http://www.artcompsci.org/#msa
It's written using Ruby but pretty easy to map into other languages etc. It covers some of the common integration approaches; Forward-Euler, Leapfrog and Hermite.
You might want to take a look at Celestia, a free space simulator. I believe that you can use it to create fictitious solar systems and it is open source.
All you need to implement is proper differential equation (Keplers law) and using Runge-Kutta. (at lest this worked for me, but there are probably better methods)
There are loads of such simulators online.
Here is one simple one implemented in 500lines of c code. (montion algorhitm is much less)
http://astro.berkeley.edu/~dperley/programs/ssms.html.
Also check this:
http://en.wikipedia.org/wiki/Kepler_problem
http://en.wikipedia.org/wiki/Two-body_problem
http://en.wikipedia.org/wiki/N-body_problem
In physics this is known as the N-Body Problem. It is famous because you can not solve this by hand for a system with more than three planets. Luckily, you can get approximate solutions with a computer very easily.
A nice paper on writing this code from the ground up can be found here.
However, I feel a word of warning is important here. You may not get the results you expect. If you want to see how:
the mass of a planet affects its orbital speed around the Sun, cool. You will see that.
the different planets interact with each other, you will be bummed.
The problem is this.
Yeah, modern astronomers are concerned with how Saturn's mass changes the Earth's orbit around the Sun. But this is a VERY minor effect. If you are going to plot the path of a planet around the Sun, it will hardly matter that there are other planets in the Solar System. The Sun is so big it will drown out all other gravity. The only exceptions to this are:
If your planets have very elliptical orbits. This will cause the planets to potentially get closer together, so they interact more.
If your planets are almost the exact same distance from the Sun. They will interact more.
If you make your planets so comically large they compete with the Sun for gravity in the outer Solar System.
To be clear, yes, you will be able to calculate some interactions between planets. But no, these interactions will not be significant to the naked eye if you create a realistic Solar System.
Try it though, and find out!
Check out nMod, a n-body modeling toolkit written in C++ and using OpenGL. It has a pretty well populated solar system model that comes with it and it should be easy to modify. Also, he has a pretty good wiki about n-body simulation in general. The same guy who created this is also making a new program called Moody, but it doesn't appear to be as far along.
In addition, if you are going to do n-body simulations with more than just a few objects, you should really look at the fast multipole method (also called the fast multipole algorithm). It can the reduce number of computations from O(N^2) to O(N) to really speed up your simulation. It is also one of the top ten most successful algorithms of the 20th century, according to the author of this article.
Algorithms to simulate planetary physics.
Here is an implementation of the Keppler parts, in my Android app. The main parts are on my web site for you can download the whole source: http://www.barrythomas.co.uk/keppler.html
This is my method for drawing the planet at the 'next' position in the orbit. Think of the steps like stepping round a circle, one degree at a time, on a circle which has the same period as the planet you are trying to track. Outside of this method I use a global double as the step counter - called dTime, which contains a number of degrees of rotation.
The key parameters passed to the method are, dEccentricty, dScalar (a scaling factor so the orbit all fits on the display), dYear (the duration of the orbit in Earth years) and to orient the orbit so that perihelion is at the right place on the dial, so to speak, dLongPeri - the Longitude of Perihelion.
drawPlanet:
public void drawPlanet (double dEccentricity, double dScalar, double dYear, Canvas canvas, Paint paint,
String sName, Bitmap bmp, double dLongPeri)
{
double dE, dr, dv, dSatX, dSatY, dSatXCorrected, dSatYCorrected;
float fX, fY;
int iSunXOffset = getWidth() / 2;
int iSunYOffset = getHeight() / 2;
// get the value of E from the angle travelled in this 'tick'
dE = getE (dTime * (1 / dYear), dEccentricity);
// get r: the length of 'radius' vector
dr = getRfromE (dE, dEccentricity, dScalar);
// calculate v - the true anomaly
dv = 2 * Math.atan (
Math.sqrt((1 + dEccentricity) / (1 - dEccentricity))
*
Math.tan(dE / 2)
);
// get X and Y coords based on the origin
dSatX = dr / Math.sin(Math.PI / 2) * Math.sin(dv);
dSatY = Math.sin((Math.PI / 2) - dv) * (dSatX / Math.sin(dv));
// now correct for Longitude of Perihelion for this planet
dSatXCorrected = dSatX * (float)Math.cos (Math.toRadians(dLongPeri)) -
dSatY * (float)Math.sin(Math.toRadians(dLongPeri));
dSatYCorrected = dSatX * (float)Math.sin (Math.toRadians(dLongPeri)) +
dSatY * (float)Math.cos(Math.toRadians(dLongPeri));
// offset the origin to nearer the centre of the display
fX = (float)dSatXCorrected + (float)iSunXOffset;
fY = (float)dSatYCorrected + (float)iSunYOffset;
if (bDrawOrbits)
{
// draw the path of the orbit travelled
paint.setColor(Color.WHITE);
paint.setStyle(Paint.Style.STROKE);
paint.setAntiAlias(true);
// get the size of the rect which encloses the elliptical orbit
dE = getE (0.0, dEccentricity);
dr = getRfromE (dE, dEccentricity, dScalar);
rectOval.bottom = (float)dr;
dE = getE (180.0, dEccentricity);
dr = getRfromE (dE, dEccentricity, dScalar);
rectOval.top = (float)(0 - dr);
// calculate minor axis from major axis and eccentricity
// http://www.1728.org/ellipse.htm
double dMajor = rectOval.bottom - rectOval.top;
double dMinor = Math.sqrt(1 - (dEccentricity * dEccentricity)) * dMajor;
rectOval.left = 0 - (float)(dMinor / 2);
rectOval.right = (float)(dMinor / 2);
rectOval.left += (float)iSunXOffset;
rectOval.right += (float)iSunXOffset;
rectOval.top += (float)iSunYOffset;
rectOval.bottom += (float)iSunYOffset;
// now correct for Longitude of Perihelion for this orbit's path
canvas.save();
canvas.rotate((float)dLongPeri, (float)iSunXOffset, (float)iSunYOffset);
canvas.drawOval(rectOval, paint);
canvas.restore();
}
int iBitmapHeight = bmp.getHeight();
canvas.drawBitmap(bmp, fX - (iBitmapHeight / 2), fY - (iBitmapHeight / 2), null);
// draw planet label
myPaint.setColor(Color.WHITE);
paint.setTextSize(30);
canvas.drawText(sName, fX+20, fY-20, paint);
}
The method above calls two further methods which provide values of E (the mean anomaly) and r, the length of the vector at the end of which the planet is found.
getE:
public double getE (double dTime, double dEccentricity)
{
// we are passed the degree count in degrees (duh)
// and the eccentricity value
// the method returns E
double dM1, dD, dE0, dE = 0; // return value E = the mean anomaly
double dM; // local value of M in radians
dM = Math.toRadians (dTime);
int iSign = 1;
if (dM > 0) iSign = 1; else iSign = -1;
dM = Math.abs(dM) / (2 * Math.PI); // Meeus, p 206, line 110
dM = (dM - (long)dM) * (2 * Math.PI) * iSign; // line 120
if (dM < 0)
dM = dM + (2 * Math.PI); // line 130
iSign = 1;
if (dM > Math.PI) iSign = -1; // line 150
if (dM > Math.PI) dM = 2 * Math.PI - dM; // line 160
dE0 = Math.PI / 2; // line 170
dD = Math.PI / 4; // line 170
for (int i = 0; i < 33; i++) // line 180
{
dM1 = dE0 - dEccentricity * Math.sin(dE0); // line 190
dE0 = dE0 + dD * Math.signum((float)(dM - dM1));
dD = dD / 2;
}
dE = dE0 * iSign;
return dE;
}
getRfromE:
public double getRfromE (double dE, double dEccentricty, double dScalar)
{
return Math.min(getWidth(), getHeight()) / 2 * dScalar * (1 - (dEccentricty * Math.cos(dE)));
}
It looks like it is very hard and requires strong knowledge of physics but in fact it is very easy, you need to know only 2 formulas and basic understanding of vectors:
Attractional force (or gravitational force) between planet1 and planet2 with mass m1 and m2 and distance between them d: Fg = G*m1*m2/d^2; Fg = m*a. G is a constant, find it by substituting random values so that acceleration "a" will not be too small and not too big approximately "0.01" or "0.1".
If you have total vector force which is acting on a current planet at that instant of time, you can find instant acceleration a=(total Force)/(mass of current planet). And if you have current acceleration and current velocity and current position, you can find new velocity and new position
If you want to look it real you can use following supereasy algorythm (pseudocode):
int n; // # of planets
Vector2D planetPosition[n];
Vector2D planetVelocity[n]; // initially set by (0, 0)
double planetMass[n];
while (true){
for (int i = 0; i < n; i++){
Vector2D totalForce = (0, 0); // acting on planet i
for (int j = 0; j < n; j++){
if (j == i)
continue; // force between some planet and itself is 0
Fg = G * planetMass[i] * planetMass[j] / distance(i, j) ^ 2;
// Fg is a scalar value representing magnitude of force acting
// between planet[i] and planet[j]
// vectorFg is a vector form of force Fg
// (planetPosition[j] - planetPosition[i]) is a vector value
// (planetPosition[j]-planetPosition[i])/(planetPosition[j]-plantetPosition[i]).magnitude() is a
// unit vector with direction from planet[i] to planet[j]
vectorFg = Fg * (planetPosition[j] - planetPosition[i]) /
(planetPosition[j] - planetPosition[i]).magnitude();
totalForce += vectorFg;
}
Vector2D acceleration = totalForce / planetMass[i];
planetVelocity[i] += acceleration;
}
// it is important to separate two for's, if you want to know why ask in the comments
for (int i = 0; i < n; i++)
planetPosition[i] += planetVelocity[i];
sleep 17 ms;
draw planets;
}
If you're simulating physics, I highly recommend Box2D.
It's a great physics simulator, and will really cut down the amount of boiler plate you'll need, with physics simulating.
Fundamentals of Astrodynamics by Bate, Muller, and White is still required reading at my alma mater for undergrad Aerospace engineers. This tends to cover the orbital mechanics of bodies in Earth orbit...but that is likely the level of physics and math you will need to start your understanding.
+1 for #Stefano Borini's suggestion for "everything that Jean Meeus has written."
Dear Friend here is the graphics code that simulate solar system
Kindly refer through it
/*Arpana*/
#include<stdio.h>
#include<graphics.h>
#include<conio.h>
#include<math.h>
#include<dos.h>
void main()
{
int i=0,j=260,k=30,l=150,m=90;
int n=230,o=10,p=280,q=220;
float pi=3.1424,a,b,c,d,e,f,g,h,z;
int gd=DETECT,gm;
initgraph(&gd,&gm,"c:\tc\bgi");
outtextxy(0,10,"SOLAR SYSTEM-Appu");
outtextxy(500,10,"press any key...");
circle(320,240,20); /* sun */
setfillstyle(1,4);
floodfill(320,240,15);
outtextxy(310,237,"sun");
circle(260,240,8);
setfillstyle(1,2);
floodfill(258,240,15);
floodfill(262,240,15);
outtextxy(240,220,"mercury");
circle(320,300,12);
setfillstyle(1,1);
floodfill(320,298,15);
floodfill(320,302,15);
outtextxy(335,300,"venus");
circle(320,160,10);
setfillstyle(1,5);
floodfill(320,161,15);
floodfill(320,159,15);
outtextxy(332,150, "earth");
circle(453,300,11);
setfillstyle(1,6);
floodfill(445,300,15);
floodfill(448,309,15);
outtextxy(458,280,"mars");
circle(520,240,14);
setfillstyle(1,7);
floodfill(519,240,15);
floodfill(521,240,15);
outtextxy(500,257,"jupiter");
circle(169,122,12);
setfillstyle(1,12);
floodfill(159,125,15);
floodfill(175,125,15);
outtextxy(130,137,"saturn");
circle(320,420,9);
setfillstyle(1,13);
floodfill(320,417,15);
floodfill(320,423,15);
outtextxy(310,400,"urenus");
circle(40,240,9);
setfillstyle(1,10);
floodfill(38,240,15);
floodfill(42,240,15);
outtextxy(25,220,"neptune");
circle(150,420,7);
setfillstyle(1,14);
floodfill(150,419,15);
floodfill(149,422,15);
outtextxy(120,430,"pluto");
getch();
while(!kbhit()) /*animation*/
{
a=(pi/180)*i;
b=(pi/180)*j;
c=(pi/180)*k;
d=(pi/180)*l;
e=(pi/180)*m;
f=(pi/180)*n;
g=(pi/180)*o;
h=(pi/180)*p;
z=(pi/180)*q;
cleardevice();
circle(320,240,20);
setfillstyle(1,4);
floodfill(320,240,15);
outtextxy(310,237,"sun");
circle(320+60*sin(a),240-35*cos(a),8);
setfillstyle(1,2);
pieslice(320+60*sin(a),240-35*cos(a),0,360,8);
circle(320+100*sin(b),240-60*cos(b),12);
setfillstyle(1,1);
pieslice(320+100*sin(b),240-60*cos(b),0,360,12);
circle(320+130*sin(c),240-80*cos(c),10);
setfillstyle(1,5);
pieslice(320+130*sin(c),240-80*cos(c),0,360,10);
circle(320+170*sin(d),240-100*cos(d),11);
setfillstyle(1,6);
pieslice(320+170*sin(d),240-100*cos(d),0,360,11);
circle(320+200*sin(e),240-130*cos(e),14);
setfillstyle(1,7);
pieslice(320+200*sin(e),240-130*cos(e),0,360,14);
circle(320+230*sin(f),240-155*cos(f),12);
setfillstyle(1,12);
pieslice(320+230*sin(f),240-155*cos(f),0,360,12);
circle(320+260*sin(g),240-180*cos(g),9);
setfillstyle(1,13);
pieslice(320+260*sin(g),240-180*cos(g),0,360,9);
circle(320+280*sin(h),240-200*cos(h),9);
setfillstyle(1,10);
pieslice(320+280*sin(h),240-200*cos(h),0,360,9);
circle(320+300*sin(z),240-220*cos(z),7);
setfillstyle(1,14);
pieslice(320+300*sin(z),240-220*cos(z),0,360,7);
delay(20);
i++;
j++;
k++;
l++;
m++;
n++;
o++;
p++;
q+=2;
}
getch();
}

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