Hi,

The sketch below produces two vector fields. Part of the third last method called calculateField() is commented out. Uncommenting that section calculates an average for theta and magnitude for the two fields and should then plot a single vector field which would be the sum of the two fields.

Firstly the fields are not summing correctly and secondly moving the charges, only one seems to effect the overall field. (The fields can be changed by holding down the left mouse button and dragging the charges around.)

1. int numCharges = 2;//the number of charges
2. Electrons[] charge = new Electrons[numCharges];//Declare the 1D array called 'charge', the elements of which are objects of the class called 'Electrons'
3. int numVectorsX = 21;//20*30 that's number of vectors across by spacing between each is width and add 1 to the number of vectors in the x-direction
4. int numVectorsY = 11;//10*30 that's number of vectors down by spacing between each is height and add 1 to the number of vectors in the y-direction
5. int distance = 30;//spacing between vectors, same for x and y directions
6. Field[][] vectors = new Field[numVectorsX][numVectorsY];//Declare the 2D array called 'vectors', the elements of which are objects of the class called 'Field'
7. float targetX = 300, targetY = 150, pol, fieldStrength, minDiameter, maxDiameter;//the field initially points to a singularity at the coordinate (300,150). targetX and targetY is where the field points to. 'pol' is the polarity of the charge
8. float theta = 0;//angle between charge and each vector
9. float magnitude = 0;//length or magnitude of a vector
10. float fieldTransparency = 0;
11. int r, g, b;//red green blue variables for charge colour
12. float Fieldstrength;
13. int countCharges = -1;
14. void setup() {
15.   size(600, 300);
16.   smooth();
17.   noStroke();
18.   for (int k = 0; k < numCharges; k++) {//these loops populate the 2D array, each element of this array is an object and each object is a vector
19.     //x, y, r, g, b, transparency, count, initial diameter, minChargediameter, maxChargediameter... the fields
20.     charge[k] = new Electrons(100 + (100*k), 100 + (50*k), 0, 0, 255, 30, 1, 100, 20, 400); //Construct the object charge
21.   }
22.   float maxdist = 400;
23.   for (int i = 0; i < numVectorsX; i++) {//these loops populate the 2D array, each element of this array is an object and each object is a vector
24.     for (int j = 0; j < numVectorsY; j++) {
25.       // fieldTransparency, xField, yField, magnitude, theta, maxdist, countCharges
26.       vectors[i][j] = new Field(fieldTransparency, i*distance, j*distance, magnitude, theta, maxdist, countCharges);
27.     }
28.   }
29. }
30. void draw() {
31.   background(#DAEBF2);
32.   for (int k = 0; k < numCharges; k++) {//these loops populate the 2D array, each element of this array is an object and each object is a vector
33.     charge[k].move();
34.     charge[k].display();
35.   }
36.   for (int i = 0; i < numVectorsX; i++) {
37.     for (int j = 0; j < numVectorsY; j++) {
38.       for (int k = 0; k < numCharges; k++) {
39.         vectors[i][j].calculateField();
40.         vectors[i][j].update(charge[k].x, charge[k].y, charge[k].diameter, charge[k].minChargediameter, charge[k].maxChargediameter);//puts the fields x, y etc. from the object 'charge' into the object 'vectors', there they are set equal to targetX, targetY, etc. which is where the field points to
41.         vectors[i][j].polarity(charge[k].r);//puts the field r from the object 'charge' into the object 'vectors', there it is set equal to 'pol'.
42.         //vectors[i][j].plotField();
43.       }
44.     }
45.   }
46. }
47. void mouseReleased() {
48.   if (mouseButton == CENTER) {
49.     for (int k = 0; k < numCharges; k++) {//these loops populate the 2D array, each element of this array is an object and each object is a vector
50.       charge[k].released();
51.     }
52.   }
53. }
54. class Electrons {
55.   float x, y, r, g, b, transparency, diameter, minChargediameter, maxChargediameter;
56.   int count;
57.   //Constructor
58.   Electrons(float xpos, float ypos, float rpos, float gpos, float bpos, float trans, int countpos, float diameterpos, float minChargediameterpos, float maxChargediameterpos) {
59.     x = xpos;
60.     y = ypos;
61.     r = rpos;
62.     g = gpos;
63.     b = bpos;
64.     transparency = trans;
65.     count = countpos;
66.     diameter = diameterpos;
67.     minChargediameter = minChargediameterpos;
68.     maxChargediameter = maxChargediameterpos;
69.   }
70.   void move() {
71.     if (((dist(mouseX, mouseY, x, y))<(diameter/2))&&(mousePressed == true)) {//tests to see if mouse is on charge
72.       if (mouseButton == LEFT) {
73.         x = mouseX;
74.         y = mouseY;
75.       }
76.       else if (mouseButton == RIGHT) {//dragging mouse toward centre decreases size of charge
77.         if (((dist(mouseX, mouseY, x, y))-(dist(pmouseX, pmouseY, x, y)))>(0)) {
78.           if (diameter < maxChargediameter) {//prevents diameter getting too big, max diameter is 400
79.             diameter = diameter + 5; //increases size of diameter
80.             transparency += 0.5;
81.           }
82.         } //dragging mouse away from center increases size of charge
83.         else if (((dist(mouseX, mouseY, x, y))-(dist(pmouseX, pmouseY, x, y)))<(0)) {
84.           if (diameter > minChargediameter) {//prevents diameter getting too small and circle disappearing, min diameter is 20
85.             diameter = diameter - 5; // decreases size of diameter
86.             transparency -= 0.5;
87.           }
88.         }
89.       }
90.     }
91.   }
92.   void display() {
93.     fill(r, g, b, transparency);//fills the charge with colours red, green, blue
94.     ellipse(x, y, diameter, diameter);//draws the charge
95.   }
96.   void released() {
97.     if (((dist(mouseX, mouseY, x, y))<(diameter/2))) {//tests to see if mouse is on charge
98.       count = (count + 1) % 2;
99.       if (count == 1) {//sets colour to blue once
100.         r = 0;
101.         b = 255;
102.       }
103.       else if (count == 0) {//set colour red to blue
104.         r = 255;
105.         b = 0;
106.       }
107.     }
108.   }
109. }
110. class Field {
111.   float fieldTransparency, xField, yField, magnitude, theta, maxdist, countCharges;
112.   //Constructor
113.   Field(float fieldTransparencypos, float xFieldpos, float yFieldpos, float magnitudepos, float thetapos, float maxdistpos, int countChargespos) {
114.     fieldTransparency =fieldTransparencypos;
115.     xField = xFieldpos;
116.     yField = yFieldpos;
117.     magnitude = magnitudepos;
118.     theta = thetapos;
119.     maxdist = maxdistpos;
120.     countCharges = countChargespos;
121.   }
122.   void calculateField() {
123.     float theta = atan((targetY-yField)/(targetX-xField));//(targetX,targetY) coordinates of the charges. (xField,yField) coordinates of point at which vector is defined.
124.     float d = (sqrt(pow(targetY-yField, 2) + pow(targetX-xField, 2)));//should be 1/r^2 but not practical here
125.     if (targetX < xField) {//without this the vectors on the left of screen will point away from charge and vectors on right of screen toward it. All should point away or toward it
126.       theta += PI;
127.     }
128.     if (pol == 0) {//if 'pol' is 0 then r = 0 in charge.released and so charge is blue and positive
129.       theta += PI; //points the field away from the charge position for a positive charge
130.     }    
131.     float maxFieldstrength, minFieldstrength = 0;
132.     float newVectorlengthmin = 10, newVectorlengthmax = 35;
133.     maxFieldstrength = map(fieldStrength, minDiameter, maxDiameter, newVectorlengthmin, newVectorlengthmax);//maps the fieldStrength, which is the diameter of the charge, from the max and mix charge diameter to the max and min charger length
134.     if (d > maxFieldstrength) {
135.       magnitude = map(d, 0, maxdist, maxFieldstrength, minFieldstrength);//the second last value is the maximum length of a vector. 2nd last value should a min and last a max value, inverting them puts longest vectors near charge
136.       fieldTransparency = map(d, 0, maxdist, 205, -20);
137.     }
138. /*    countCharges = (countCharges + 1) % numCharges;
139.     if (countCharges != 0) {
140.       fieldTransparency += fieldTransparency;
141.       theta += theta;//sums theta
142.       magnitude += magnitude;//sums theta
143.     }
144.     if (countCharges == 0) {
145.       fieldTransparency = fieldTransparency/numCharges;//calculates average
146.       theta = theta/numCharges;//calculates average
147.       magnitude = magnitude/numCharges;//calculates average
148. */
149.       stroke(1, fieldTransparency);
150.       fill(0, 0, 0);
151.       pushMatrix();
152.       translate(xField, yField);
153.       rotate(theta);
154.       line(0, 0, magnitude, 0);
155.       beginShape();//this shape is the arrow heads of the vectors
156.       vertex(magnitude, -3);
157.       vertex(magnitude, 3);
158.       vertex(magnitude + 3, 0);
159.       endShape(CLOSE);
160.       popMatrix();
161.       noFill();
162.       noStroke();
163.     //} THIS BRACKET IS COMMENTED OUT
164.   }
165.   void update(float x, float y, float diameter, float minChargediameter, float maxChargediameter) {//this method transfers fields x, y, diameter, ... etc from the class Electrons to the class Field
166.     targetX = x;//x-coordinate of charge
167.     targetY = y;//y-coordinate of charge
168.     fieldStrength = diameter;
169.     minDiameter = minChargediameter;
170.     maxDiameter = maxChargediameter;
171.   }
172.   void polarity(float r) {
173.     pol = r;
174.   }
175. }

Any help would be greatly appreciated.

Thanks,

Shane