How can I draw a spline curves with c in codeblocks?

Question

I am trying to draw a minimum enclosing circle and I need spline curves for points. but also I shouldn't use libraries. For preview, I used lines but they need curves. How can I fix it?

Which one is true arc, line or points?

#include <stdio.h>
#include <graphics.h>
#include <math.h>
#include <conio.h>

struct nokta
{
    int x,y;
};
//-------------------------------------------------------------//

int main()
{
    int gd = DETECT;
    int gm;
    initgraph(&gd, &gm, "C:\\TC\\BGI");
    initwindow(800,800);
    struct nokta noktalar[50];
    FILE *noktaal=fopen("noktalar.txt","r");
    int i=0;
    int sayac=0;
    if(noktaal==NULL)
    {
        printf("Dosya yok");
    }
    while(!feof(noktaal))
    {

        fscanf(noktaal,"%d %d",&noktalar[i].x,&noktalar[i].y);
        sayac++;
        i++;
    };

    for(int i=0; i<sayac-1; i++)
    {
        printf("%d %d \n",noktalar[i].x,noktalar[i].y);
    }
    fclose(noktaal);

//----------------------------------------------------------------//
    if(sayac==1)//If there is no point
    {
        printf("Lutfen koordinat giriniz.");
    }

    if(sayac==2)// If there is one point
    {
        printf("Lutfen birden fazla koordinat giriniz.");
    }

    if(sayac==3)//If there is two point
    {
        int uzunluk1=abs(noktalar[1].x-noktalar[0].x);
        int uzunluk2=abs(noktalar[1].y-noktalar[0].y);
        double yaricap=sqrt(pow(uzunluk1,2)+pow(uzunluk2,2));
        float merkezx=(noktalar[1].x+noktalar[0].x)/2.0;
        float merkezy=(noktalar[1].y+noktalar[0].y)/2.0;
        printf("Yaricap:%.2f\n",yaricap/2);
        printf("Merkez noktasi:{%.2f,%.2f}",merkezx,merkezy);
        line(getmaxx()/2,0,getmaxx()/2,getmaxy());//y düzlemi
        line(0,getmaxy()/2,getmaxx(),getmaxy()/2);//x düzlemi
        putpixel(((getmaxx()/2)+(noktalar[0].x*20)),(getmaxy()/2)-(noktalar[0].y*20),GREEN);
        putpixel(((getmaxx()/2)+(noktalar[1].x*20)),(getmaxy()/2)-(noktalar[1].y*20),GREEN);
        for(int i=20; i<=800; i=i+20)
        {
            line(i,getmaxy()/2.03,i,getmaxy()/1.97);
        }
        for(int i=20; i<=800; i=i+20)
        {
            line(getmaxx()/2.03,i,getmaxx()/1.97,i);
        }
        circle((getmaxx()/2)+(merkezx*20),(getmaxy()/2)-(merkezy*20),yaricap*7.9);
        getch();
        closegraph();
    }

    if(sayac>3)//If there is three or more points.
    {
        int karetoplam;
        double enbuyuk=1.0,yaricap1;
        float merkez1x,merkez1y;
        int sayac1=0;
        int ikinoktauzakligi=0;
        for(int i=0; i<sayac-1; i++)
        {
            for(int j=0; j<sayac-1; j++)
            {
                float ykare=pow(abs(noktalar[i].y-noktalar[j].y),2);
                float xkare=pow(abs(noktalar[i].x-noktalar[j].x),2);
                karetoplam=ykare+xkare;
                if(enbuyuk<=karetoplam)
                {
                    enbuyuk=karetoplam;
                }
                if(enbuyuk==karetoplam)
                {
                    merkez1x=(noktalar[i].x+noktalar[j].x)/2.0;
                    merkez1y=(noktalar[i].y+noktalar[j].y)/2.0;
                    ++sayac1;
                }
            }
        }

        if(sayac1>=2)
        {
            double cap1=sqrt(enbuyuk);
            yaricap1=cap1/2;
            printf("Ilk yari capi:%.2f\n",yaricap1);
            printf("Ilk merkez noktasi:{%.2f,%.2f}\n",merkez1x,merkez1y);
            line(getmaxx()/2,0,getmaxx()/2,getmaxy());//y düzlemi
            line(0,getmaxy()/2,getmaxx(),getmaxy()/2);//x düzlemi
            for(int i=20; i<=800; i=i+20)
            {
                line(i,getmaxy()/2.03,i,getmaxy()/1.97);
            }
            for(int i=20; i<=800; i=i+20)
            {
                line(getmaxx()/2.03,i,getmaxx()/1.97,i);
            }
            for(int i=0; i<sayac-1; i++)
            {
                for(int j=0; j<sayac-1; j++)
                {
                    putpixel((getmaxx()/2)+(noktalar[i].x*20),(getmaxy()/2)-(noktalar[i].y*20),GREEN);
                }
            }
            float uzunluk2;
            float arttir=0.0;
            float enbuyuk2=0.0;
            for(int i=0; i<100;i++)
            {
            for(int j=0; j<sayac-1; j++)
            {
                uzunluk2=sqrt((pow(noktalar[j].x,2)+pow(noktalar[j].y,2))-(pow(merkez1x,2)+pow(merkez1y,2)));
                if(enbuyuk2<uzunluk2)
                {
                    enbuyuk2=uzunluk2;
                }
                if(yaricap1<enbuyuk2)
                {
                    yaricap1=yaricap1+0.1;
                    arttir=arttir+0.1;
                }
            }
            }

            printf("Son yari capi:%.2f\n",yaricap1);
            printf("Son merkez noktasi:{%.2f,%.2f}",merkez1x+arttir,merkez1y+arttir);
            int uzunluk3;
            int enkucuk3=0;
            for(i=0;i<sayac-1;i++)
            {
                  line((getmaxx()/2)+(noktalar[i].x*20),((getmaxy()/2)+(noktalar[i].y*20)),((getmaxx()/2)+(noktalar[i+1].x*20)),((getmaxy()/2)+(noktalar[i+1].y*20)));
            }
            circle((getmaxx()/2)+((merkez1x+arttir)*20),(getmaxy()/2)-((merkez1y+arttir)*20),yaricap1*20);
            getch();
            closegraph();
        }

    }
}
//-------------------------------------------------------------------//

Minimum enclosing circle can be drawn with this but it doesn't show a curve. I need to show curves without libraries.