Using Splines for charts with smooth graph

1//These are all the different functions for the Splines and the Bezier Curve.
2//In order to plot the graph on any display call this in main():
3/*
4for(double t = 0; t < dataLength - 1; t += 0.001){
5  Point pixel;
6  pixel = [SplineFunction](arr,[if needed: extra arguments,] dataLength,t);
7  display.drawPixel(pixel.x, pixel.y);
8*/
9
10struct Point{
11  double x;
12  double y;
13};
14
15//You also have to define a array of Points to pass to the functions.
16
17Point Bezier(Point p0,Point p1,Point p2,Point p3,double t){
18  double x =  p0.x +
19              t * (-3 * p0.x + 3 * p1.x) +
20              pow(t,2) * (3 * p0.x - 6 * p1.x + 3 * p2.x) +
21              pow(t,3) * (-1 * p0.x + 3 * p1.x - 3 * p2.x + p3.x);
22
23  double y =  p0.y +
24              t * (-3 * p0.y + 3 * p1.y) +
25              pow(t,2) * (3 * p0.y - 6 * p1.y + 3 * p2.y) +
26              pow(t,3) * (-1 * p0.y + 3 * p1.y - 3 * p2.y + p3.y);
27
28  return {x,y};
29}
30
31Point Hermite(Point* data, Point v0, Point v1, int dataLength, double t){
32  int i = t;
33  
34  Point p0 = data[i];  
35  Point p1 = data[i+1];
36  static Point lastv1;
37  
38  if(v0.x + v0.y + v1.x + v1.y == 0){
39    Point pm1 = data[max(0,i-1)];
40    Point p2 = data[min(dataLength,i+2)];
41    v0 = {(p1.x - pm1.x) / 2 , (p1.y - pm1.y) / 2 };
42    v1 = {(p2.x - p0.x) / 2 , (p2.y - p0.y) / 2 };
43  }
44  else if(i > 0){
45    v0 = lastv1;
46    lastv1 = v1;
47  }
48
49 
50  t = t - (double)i;
51  double x =  p0.x +
52              t * v0.x +
53              pow(t,2) * (-3 * p0.x - 2 * v0.x + 3 * p1.x - v1.x) +
54              pow(t,3) * (2 * p0.x + v0.x - 2 * p1.x + v1.x);
55
56  double y =  p0.y +
57              t * v0.y +
58              pow(t,2) * (-3 * p0.y - 2 * v0.y + 3 * p1.y - v1.y) +
59              pow(t,3) * (2 * p0.y + v0.y - 2 * p1.y + v1.y);
60
61  return {x,y};
62}
63
64
65
66
67
68Point CatmullRom(Point* data, int dataLength, double t){
69  int i = t;
70  Point p0;
71  Point p1 = data[i];
72  Point p2 = data[i+1];
73  Point p3;
74  if(i == 0){
75    p0 = p1;
76  }
77  else{
78    p0 = data[i-1];
79  }  
80  if(i >= dataLength - 2){
81    p3 = p2;
82  }
83  else{
84    p3 = data[i+2];
85  }  
86  t = t - (double)i;  
87  double x =  (2 * p1.x +
88              t * (- p0.x + p2.x) +
89              pow(t,2) * (2 * p0.x - 5 * p1.x + 4 * p2.x - p3.x) +
90              pow(t,3) * (- p0.x + 3 * p1.x - 3 * p2.x + p3.x)) / 2;
91
92  double y =  (2 * p1.y +
93              t * (- p0.y + p2.y) +
94              pow(t,2) * (2 * p0.y - 5 * p1.y + 4 * p2.y - p3.y) +
95              pow(t,3) * (- p0.y + 3 * p1.y - 3 * p2.y + p3.y)) / 2;
96  return {x,y};
97}
98
99Point Cardinal(Point* data, double s, int dataLength, double t){
100  int i = t;
101  Point p0;
102  Point p1 = data[i];
103  Point p2 = data[i+1];
104  Point p3;
105  if(i == 0){
106    p0 = p1;
107  }
108  else{
109    p0 = data[i-1];
110  }  
111  if(i >= dataLength - 2){
112    p3 = p2;
113  }
114  else{
115    p3 = data[i+2];
116  }  
117  t = t - (double)i;  
118  double x =  p1.x +
119              t * (- s * p0.x + s * p2.x) +
120              pow(t,2) * (2 * s * p0.x + (s-3) * p1.x + (3-2*s) * p2.x - s * p3.x) +
121              pow(t,3) * (- s * p0.x + (2-s) * p1.x + (s-2) * p2.x + s * p3.x);
122
123  double y =  p1.y +
124              t * (- s * p0.y + s * p2.y) +
125              pow(t,2) * (2 * s * p0.y + (s-3) * p1.y + (3-2*s) * p2.y - s * p3.y) +
126              pow(t,3) * (- s * p0.y + (2-s) * p1.y + (s-2) * p2.y + s * p3.y);
127
128  return {x,y};
129}
130
131Point BSpline(Point* data, int dataLength, double t){
132  int i = t;
133  Point p0;
134  Point p1 = data[i];
135  Point p2 = data[i+1];
136  Point p3;
137  if(i == 0){
138    p0 = p1;
139  }
140  else{
141    p0 = data[i-1];
142  }  
143  if(i >= dataLength - 2){
144    p3 = p2;
145  }
146  else{
147    p3 = data[i+2];
148  }  
149  t = t - (double)i;
150  double x =  (p0.x + 4 * p1.x + p2.x +
151              t * (-3 * p0.x + 3 * p2.x) +
152              pow(t,2) * (3 * p0.x - 6 * p1.x + 3 * p2.x) +
153              pow(t,3) * (- p0.x + 3 * p1.x - 3 * p2.x + p3.x)) / 6;
154
155  double y =  (p0.y + 4 * p1.y + p2.y +
156              t * (-3 * p0.y + 3 * p2.y) +
157              pow(t,2) * (3 * p0.y - 6 * p1.y + 3 * p2.y) +
158              pow(t,3) * (- p0.y + 3 * p1.y - 3 * p2.y + p3.y)) / 6;
159
160  return {x,y}; 
161}