Bézier Kurve Karte x, y Punkte auf Bildschirm

Question

Hallo vor kurzem implementierte ich die Bezier-Kurve funktioniert es gut, aber mein Problem ist, ich weiß nicht, wie x, y Punkte auf dem Bildschirm, weil es mir x, y in Form von Dezimalzahlen gibt Punkte Ich werde jede Hilfe zu schätzen wissen das ist mein Code, der funktioniert, denke ich.

 import java.util.ArrayList; 


    public class Bezier { 

     public static void main(String[] args) { 
      ArrayList<Point> CP = new ArrayList<Point>(); 
      CP.add(new Point(-5, 0)); 
      CP.add(new Point(0, 5)); 
      CP.add(new Point(5, 0)); 
      CP.add(new Point(0,-5)); 


      Bezier curve = new Bezier(3, 0, 0.01, CP); 
      curve.DefineBezierCurve(); 

      ArrayList<Point>Results = curve.getCurvePoints(); 

      for(int i = 0; i<Results.size() ; i++){ 
       Point x = Results.get(i); 
       System.out.println(x.Y); 
      } 


     } 
    // class definitions 
     private ArrayList<Point> controlPoints;// the control points 
     private double t;//the value of t indicates the location of the point on the line sigment 
     private double step;// the increment value that the t increments 
     private int N;//the Beziar Curve Order 
     private ArrayList<Point>CurvePoints;// genrated (x,y) values of the curve 

    // constructor 
     public Bezier(int n , double t , double step ,ArrayList<Point> CP){ 
      this.N = n ; 
      this.t = t; 
      this.step = step; 
      this.controlPoints = CP; 
      CurvePoints = new ArrayList<Point>(); 
     } 

     private int factorial(int x){ 
      int result =1; 
      for(int i= x ; x>0 ; x--){ 
       result*=x; 
      } 
      return result; 
     } 
     private int BinomialCoefficient(int i){ 
      // we get the order form the global variable 
      int factN = factorial(this.N); 
      int factI = factorial(i); 
      int factN_I = factorial(this.N-i); 
      int theCoefficient = (factN/(factI*factN_I)); 
      return theCoefficient ; 
     } 
     private Point BI_N_P(int i){ 
      int coefficient = BinomialCoefficient(i); 
      Point CurrentControlPoint = this.controlPoints.get(i); 
      double X = coefficient* Math.pow(t,i)* Math.pow((1-t),(this.N-i))*CurrentControlPoint.X ; 
      double Y = coefficient* Math.pow(t,i)* Math.pow((1-t),(this.N-i))*CurrentControlPoint.Y ; 
      Point Tmp = new Point(X, Y); 
      return Tmp; 
    //  this.CurvePoints.add(PointOnCrve); 
     } 
     private void DefineBezierCurve(){ 
      while(t<=1){ 
       Point PointOnCurve = new Point(0, 0); 
       for(int i = 0 ; i<=this.N ; i++){ 
        Point tmp = BI_N_P(i); 
        PointOnCurve.X+=tmp.X; 
        PointOnCurve.Y+=tmp.Y; 
       } 
       this.CurvePoints.add(PointOnCurve); 
       this.t+=this.step; 
      } 
     } 

     public ArrayList<Point> getCurvePoints(){ 
      return this.CurvePoints; 
     } 

    } 
    class Point{  
     public double X; 
     public double Y; 
     public Point(double x,double y){ 
      X=x; 
      Y=y; 
     } 
    } 

verwendete ich die genrated Punkte sie in Excel zu ziehen, und dies war mein Ergebnis

Beispiel kubische Bezierkurve Anfangs t = 0, Schritt = 0,01, mit Kontrollpunkten (-5, 0), (0, 5), (5, 0), (0, -5) erzeugten Punkte X

-5.0 
-4.85001 
-4.700079999999999 
-4.55027 
-4.400639999999999 
-4.25125 
-4.102159999999999 
-3.9534299999999996 
-3.80512 
-3.6572900000000006 
-3.5100000000000007 
-3.3633100000000002 
-3.2172800000000006 
-3.07197 
-2.92744 
-2.7837499999999995 
-2.6409599999999993 
-2.4991299999999996 
-2.3583199999999995 
-2.2185899999999994 
-2.0799999999999996 
-1.9426099999999988 
-1.8064799999999992 
-1.6716699999999989 
-1.5382399999999987 
-1.4062499999999998 
-1.2757599999999993 
-1.1468299999999993 
-1.0195199999999995 
-0.8938899999999995 
-0.7699999999999991 
-0.6479099999999991 
-0.527679999999999 
-0.4093699999999989 
-0.29303999999999886 
-0.17874999999999885 
-0.06655999999999862 
0.043470000000001674 
0.15128000000000164 
0.256810000000002 
0.3600000000000019 
0.4607900000000018 
0.5591200000000022 
0.6549300000000019 
0.7481600000000019 
0.838750000000002 
0.9266400000000021 
1.011770000000002 
1.094080000000002 
1.173510000000002 
1.2500000000000018 
1.3234900000000016 
1.3939200000000018 
1.4612300000000018 
1.5253600000000018 
1.5862500000000017 
1.6438400000000017 
1.6980700000000017 
1.7488800000000018 
1.7962100000000016 
1.8400000000000019 
1.8801900000000014 
1.916720000000001 
1.9495300000000007 
1.9785600000000012 
2.0037500000000006 
2.0250400000000006 
2.042370000000001 
2.05568 
2.0649100000000002 
2.0700000000000003 
2.07089 
2.06752 
2.0598299999999994 
2.0477599999999994 
2.031249999999999 
2.010239999999999 
1.984669999999999 
1.9544799999999984 
1.9196099999999983 
1.8799999999999981 
1.8355899999999976 
1.7863199999999972 
1.7321299999999973 
1.672959999999997 
1.6087499999999963 
1.539439999999996 
1.4649699999999957 
1.3852799999999954 
1.3003099999999952 
1.2099999999999946 
1.1142899999999942 
1.0131199999999938 
0.9064299999999934 
0.7941599999999929 
0.6762499999999925 
0.552639999999992 
0.4232699999999916 
0.28807999999999107 
0.14700999999999054 

erzeugten Y-Punkte

0.0 
0.14701 
0.28808 
0.42327 
0.55264 
0.6762500000000001 
0.79416 
0.90643 
1.0131200000000002 
1.1142900000000002 
1.21 
1.3003099999999999 
1.3852799999999996 
1.4649699999999997 
1.5394399999999997 
1.6087499999999997 
1.6729599999999996 
1.7321299999999997 
1.78632 
1.83559 
1.88 
1.91961 
1.95448 
1.98467 
2.0102400000000005 
2.0312500000000004 
2.0477600000000002 
2.0598300000000003 
2.0675200000000005 
2.0708900000000003 
2.0700000000000003 
2.0649100000000002 
2.0556800000000006 
2.0423700000000005 
2.0250400000000006 
2.00375 
1.9785599999999997 
1.9495300000000002 
1.91672 
1.8801899999999998 
1.8399999999999999 
1.7962099999999999 
1.748879999999999 
1.6980699999999993 
1.6438399999999993 
1.5862499999999993 
1.5253599999999992 
1.461229999999999 
1.3939199999999987 
1.3234899999999983 
1.2499999999999982 
1.173509999999998 
1.094079999999998 
1.011769999999998 
0.9266399999999977 
0.8387499999999977 
0.7481599999999973 
0.6549299999999975 
0.5591199999999971 
0.46078999999999715 
0.359999999999997 
0.2568099999999969 
0.15127999999999653 
0.043469999999996345 
-0.06656000000000395 
-0.17875000000000396 
-0.2930400000000042 
-0.40937000000000445 
-0.5276800000000048 
-0.6479100000000048 
-0.7700000000000049 
-0.8938900000000052 
-1.0195200000000053 
-1.1468300000000053 
-1.2757600000000053 
-1.4062500000000062 
-1.538240000000006 
-1.6716700000000062 
-1.8064800000000063 
-1.9426100000000066 
-2.0800000000000067 
-2.218590000000007 
-2.3583200000000066 
-2.499130000000007 
-2.6409600000000077 
-2.783750000000008 
-2.927440000000008 
-3.0719700000000083 
-3.217280000000008 
-3.363310000000008 
-3.5100000000000087 
-3.6572900000000086 
-3.805120000000009 
-3.9534300000000084 
-4.102160000000009 
-4.251250000000009 
-4.40064000000001 
-4.550270000000009 
-4.7000800000000105 
-4.85001000000001 

Answer 1

Multiplizieren Sie die Menge der Punkte mit einem Skalierungsfaktor und runden Sie dann zu einer ganzen Zahl. Ich würde vorschlagen, den Faktor Screen Width/MAX(list of x points) für x, und Screen Height/MAX(list of y points) für y. Dies sollte Ihnen eine Liste von Punkten geben, die auf die aktuelle Größe des Bildschirms skaliert werden. Hier ist ein Python-Code, der die Idee implementiert.

X = "-5.0 -4.85001 -4.700079999999999 -4.55027 -4.400639999999999 -4.25125 -4.102159999999999 -3.9534299999999996 -3.80512 -3.6572900000000006 -3.5100000000000007 -3.3633100000000002 -3.2172800000000006 -3.07197 -2.92744 -2.7837499999999995 -2.6409599999999993 -2.4991299999999996 -2.3583199999999995 -2.2185899999999994 -2.0799999999999996 -1.9426099999999988 -1.8064799999999992 -1.6716699999999989 -1.5382399999999987 -1.4062499999999998 -1.2757599999999993 -1.1468299999999993 -1.0195199999999995 -0.8938899999999995 -0.7699999999999991 -0.6479099999999991 -0.527679999999999 -0.4093699999999989 -0.29303999999999886 -0.17874999999999885 -0.06655999999999862 0.043470000000001674 0.15128000000000164 0.256810000000002 0.3600000000000019 0.4607900000000018 0.5591200000000022 0.6549300000000019 0.7481600000000019 0.838750000000002 0.9266400000000021 1.011770000000002 1.094080000000002 1.173510000000002 1.2500000000000018 1.3234900000000016 1.3939200000000018 1.4612300000000018 1.5253600000000018 1.5862500000000017 1.6438400000000017 1.6980700000000017 1.7488800000000018 1.7962100000000016 1.8400000000000019 1.8801900000000014 1.916720000000001 1.9495300000000007 1.9785600000000012 2.0037500000000006 2.0250400000000006 2.042370000000001 2.05568 2.0649100000000002 2.0700000000000003 2.07089 2.06752 2.0598299999999994 2.0477599999999994 2.031249999999999 2.010239999999999 1.984669999999999 1.9544799999999984 1.9196099999999983 1.8799999999999981 1.8355899999999976 1.7863199999999972 1.7321299999999973 1.672959999999997 1.6087499999999963 1.539439999999996 1.4649699999999957 1.3852799999999954 1.3003099999999952 1.2099999999999946 1.1142899999999942 1.0131199999999938 0.9064299999999934 0.7941599999999929 0.6762499999999925 0.552639999999992 0.4232699999999916 0.28807999999999107 0.14700999999999054" 
X = X.split(" "); 
absX = list(); 
for x in X: 
    absX.append(abs(float(x))); 
max_X = max(absX); 
min_X = min(X); 
screen_width = 1024; 
scale_factor = screen_width/float(max_X + float(max(X))); 
newX = list(); 
for x in X: 
    x = int(float(x)*scale_factor) + screen_width; 
    newX.append(x) 
print(newX); 

Diese gibt die folgende Liste der X-Koordinaten:

[300, 322, 344, 366, 387, 409, 430, 452, 473, 495, 516, 537, 559, 580, 601, 621, 642, 663, 683, 703, 723, 743, 763, 782, 802, 821, 840, 858, 877, 895, 913, 931, 948, 965, 982, 999, 1015, 1030, 1045, 1061, 1076, 1090, 1104, 1118, 1132, 1145, 1158, 1170, 1182, 1193, 1205, 1215, 1225, 1235, 1244, 1253, 1262, 1269, 1277, 1284, 1290, 1296, 1301, 1306, 1310, 1314, 1317, 1319, 1321, 1323, 1323, 1323, 1323, 1322, 1320, 1318, 1315, 1311, 1307, 1301, 1296, 1289, 1282, 1274, 1266, 1256, 1246, 1236, 1224, 1212, 1199, 1185, 1170, 1155, 1139, 1121, 1104, 1085, 1065, 1045] 

Und hier ist das Y:

[768, 784, 799, 814, 829, 843, 856, 868, 880, 891, 902, 912, 921, 930, 938, 946, 953, 960, 966, 971, 976, 981, 984, 988, 991, 993, 995, 996, 997, 997, 997, 997, 996, 994, 992, 990, 987, 984, 980, 976, 972, 967, 962, 956, 950, 944, 937, 930, 922, 914, 906, 898, 889, 880, 870, 861, 851, 840, 830, 819, 807, 796, 784, 772, 761, 749, 736, 723, 710, 697, 683, 669, 655, 641, 627, 612, 598, 583, 568, 553, 538, 522, 507, 491, 475, 460, 444, 428, 411, 395, 379, 363, 346, 330, 313, 297, 280, 264, 247, 230] 

Dieses Skript ist nicht perfekt und kehrt nicht die Werte innerhalb des korrekten Bereich, aber es sollte Ihnen eine Idee geben, wo Sie anfangen sollen.