java - 贝塞尔曲线图 x,y 指向屏幕

Question

嗨，最近我实现了贝塞尔曲线，它工作得很好，但我的问题是我不知道如何将 x,y 点映射到屏幕，因为它给了我小数点形式的 x,y 我将不胜感激任何帮助这是我的代码，我认为它有效。

        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;
        }
    }

我使用生成的点在 Excel 中绘制它们，这是我的结果

三次贝塞尔曲线示例初始 t=0,step = 0.01 ，带有控制点(-5, 0),(0, 5),(5, 0),(0,-5)生成X点

-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

生成的Y点

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

将点集乘以某个比例因子，然后舍入为整数。我建议 x 的系数为屏幕宽度/MAX(x 点列表)，y 的系数为屏幕高度/MAX(y 点列表)。这将为您提供一个缩放到屏幕当前尺寸的点列表。下面是一些实现这个想法的 Python 代码。

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);

这将返回以下 X 坐标列表:

[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]

这是 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]

此脚本并不完美，并且不会返回正确范围内的值，但它应该可以让您了解从哪里开始。