// TBezierInterpolation.c
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include <stdbool.h>
#include <float.h>
 
#define RESOLUTION 32
#define  POINTS_LEN 10
 
typedef struct
{
    double x, y;
}Point2D;
 
 
Point2D Point2DAdd( Point2D *left,  Point2D *right)
{
    Point2D newPoint = {left->x + right->x, left->y + right->y};
    return newPoint;
}
Point2D Point2DSubtract( Point2D *left,  Point2D *right)
{
    Point2D newPoint = {left->x - right->x, left->y - right->y};
    return newPoint;
}
Point2D Point2DMultiply( Point2D *left, double v)
{
    Point2D newPoint = {left->x * v, left->y * v};
    return newPoint;
}
 
 
void Point2DNormalize(Point2D *point)
{
    double l = sqrt(point->x * point->x + point->y * point->y);
    point->x /= l;
    point->y /= l;
}
 
 
typedef struct
{
    Point2D points[4];
}Segment;
 
void SegmentCalc(Segment *seg,double t, Point2D *p)
{
    double t2 = t * t;
    double t3 = t2 * t;
    double nt = 1.0 - t;
    double nt2 = nt * nt;
    double nt3 = nt2 * nt;
    p->x = nt3 * seg->points[0].x + 3.0 * t * nt2 * seg->points[1].x + 3.0 * t2 * nt * seg->points[2].x + t3 * seg->points[3].x;
    p->y = nt3 * seg->points[0].y + 3.0 * t * nt2 * seg->points[1].y + 3.0 * t2 * nt * seg->points[2].y + t3 * seg->points[3].y;
}
 
 
bool CalculateSpline( Point2D values[], int valuesSize, Segment bezier[])
{
    int n = valuesSize - 1;
 
    if (valuesSize < 2)
        return false;
 
    Point2D tgL= {0.0,0.0};
    Point2D tgR= {0.0,0.0};
    Point2D cur= {0.0,0.0};
    Point2D next = Point2DSubtract(&values[1] ,&values[0]);
    Point2D tmpPoint= {0.0,0.0};
    Point2DNormalize(&next);
 
    double l1 = 0.0, l2= 0.0, tmp= 0.0, x= 0.0;
 
    --n;
 
    for (int i = 0; i < n; ++i)
    {
        bezier[i].points[0] = bezier[i].points[1] = values[i];
        bezier[i].points[2] = bezier[i].points[3] = values[i + 1];
 
        cur = next;
        next = Point2DSubtract(&values[i + 2],&values[i + 1]);
        Point2DNormalize(&next);
 
        tgL = tgR;
 
        tgR = Point2DAdd(&cur,&next);
        Point2DNormalize(&tgR);
 
        if (abs(values[i + 1].y - values[i].y) < DBL_EPSILON)
        {
            l1 = l2 = 0.0;
        }
        else
        {
            tmp = values[i + 1].x - values[i].x;
            l1 = abs(tgL.x) > DBL_EPSILON ? tmp / (2.0 * tgL.x) : 1.0;
            l2 = abs(tgR.x) > DBL_EPSILON ? tmp / (2.0 * tgR.x) : 1.0;
        }
 
        if (abs(tgL.x) > DBL_EPSILON && abs(tgR.x) > DBL_EPSILON)
        {
            tmp = tgL.y / tgL.x - tgR.y / tgR.x;
            if (abs(tmp) > DBL_EPSILON)
            {
                x = (values[i + 1].y - tgR.y / tgR.x * values[i + 1].x - values[i].y + tgL.y / tgL.x * values[i].x) / tmp;
                if (x > values[i].x && x < values[i + 1].x)
                {
                    if (tgL.y > 0.0)
                    {
                        if (l1 > l2)
                            l1 = 0.0;
                        else
                            l2 = 0.0;
                    }
                    else
                    {
                        if (l1 < l2)
                            l1 = 0.0;
                        else
                            l2 = 0.0;
                    }
                }
            }
        }
        tmpPoint = Point2DMultiply(&tgL , l1);
        bezier[i].points[1] = Point2DAdd(& bezier[i].points[1],&tmpPoint);
        tmpPoint = Point2DMultiply(&tgR , l2);
        bezier[i].points[2] = Point2DSubtract(& bezier[i].points[2],&tmpPoint);
    }
 
    l1 = abs(tgL.x) > DBL_EPSILON ? (values[n + 1].x - values[n].x) / (2.0 * tgL.x) : 1.0;
 
    bezier[n].points[0] = bezier[n].points[1] = values[n];
    bezier[n].points[2] = bezier[n].points[3] = values[n + 1];
    tmpPoint = Point2DMultiply(&tgR , l1);
    bezier[n].points[1] = Point2DAdd(& bezier[n].points[1],&tmpPoint);
 
    return true;
}
 
int main()
{
 
    Point2D testValues[POINTS_LEN] = {{0.0, 0.0},
                               {20.0, 0.0},
                               {45.0, -47.0},
                               {53.0, 335.0},
                               {57.0, 26.0},
                               {62.0, 387.0},
                               { 74.0, 104.0},
                              { 89.0, 0.0},
                             {95.0, 100.0},
                             { 100.0, 0.0} };
    Segment spline[100];
 
    Point2D p = {0.0,0.0};
 
 
    CalculateSpline(testValues,POINTS_LEN, spline);
 
    for(int i = 0; i < POINTS_LEN - 1;i++)
    {
        for (int j = 0; j < RESOLUTION; j++)
        {
            SegmentCalc(&spline[i],(double)j / (double)RESOLUTION, &p);
            printf("%lf %lf\n", p.x, p.y);
        }
    }
 
    printf("%lf %lf\n", testValues[POINTS_LEN - 1].x,testValues[POINTS_LEN - 1].y);
 
    return 0;
}
 

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