KochCurve.cpp

#include "raylib.h"
#include "raymath.h"
#define RAYGUI_IMPLEMENTATION
#include "raygui.h"
#include <iostream>
#include <deque> //for deque
#include <cmath> //for atan2

using namespace std;

struct line {
    Vector2 startpt;
    Vector2 endpt;
    Color color;
};

Vector2 Vector2Rotate(Vector2 vec, float angle) {
    float len=Vector2Length(vec);
    float theta=atan2(vec.y,vec.x);
    Vector2 rval={len*cos(theta+angle),len*sin(theta+angle)};
    return rval;
}

int main()
{
    //Initialize Raylib
    InitWindow(1000, 900, "Koch Curve");
    SetWindowPosition(500,50);

    Camera camera = { 0 };
    camera.position = (Vector3){10.0, 0.0, 10.0};
    camera.target=(Vector3){0.0,0.0,0.0};
    camera.up = (Vector3){ 0.0f, 1.0f, 0.0f };
    camera.fovy = 60.0f;
    camera.projection = CAMERA_PERSPECTIVE;
    SetCameraMode(camera,CAMERA_FREE);
    SetTargetFPS(30);

    line linetemp, linenew;
    Vector2 midpt1, midpt2;
    uint vsize, counter=0;
    int levels=2, oldlevels=2;
    bool draw_analysis=false;

    deque<line> LineList;
    // Draw our initial figure
    line initiator = {(Vector2){200,200},(Vector2){800,200},BLUE};
    LineList.push_back(initiator);
    initiator = {(Vector2){800,200},(Vector2){500,200+600*sqrt(3.0)/2.0},BLUE};
    LineList.push_back(initiator);
    initiator = {(Vector2){500,200+600*sqrt(3.0)/2.0},(Vector2){200,200},BLUE};
    LineList.push_back(initiator);

    while (!WindowShouldClose()){
//Update

        levels=(int)GuiSlider({900,50,60,40},"Levels",levels,1.0,9.0,true);  //Note: at 10 levels there are 786K lines, so FPS starts to drop.  We are beyond visual resolution >8
        if (levels!=oldlevels) {    //If the user changes recursion level, clear counter, clear deque list, and reset initial drawing
            counter=0;
            oldlevels=levels;
            LineList.clear();
            initiator = {(Vector2){200,200},(Vector2){800,200},BLUE};
            LineList.push_back(initiator);
            initiator = {(Vector2){800,200},(Vector2){500,200+600*sqrt(3.0)/2.0},BLUE};
            LineList.push_back(initiator);
            initiator = {(Vector2){500,200+600*sqrt(3.0)/2.0},(Vector2){200,200},BLUE};
            LineList.push_back(initiator);
        }

        draw_analysis=GuiCheckBox({900,100,20,20},"Analysis",draw_analysis);

        counter++;
        if (counter<levels) {
            vsize=LineList.size(); //Need to capture LineList.size() here to make one pass through existing deque items and not new ones we add this cycle
            for (uint i=0;i<vsize;i++) {
                linetemp = LineList.front();
                LineList.pop_front();
                midpt1=Vector2Add(linetemp.startpt,Vector2Scale(Vector2Subtract(linetemp.endpt,linetemp.startpt),1.0/3.0)); //Trisect the line
                midpt2=Vector2Add(linetemp.startpt,Vector2Scale(Vector2Subtract(linetemp.endpt,linetemp.startpt),2.0/3.0));
                linenew={linetemp.startpt,midpt1,BLUE}; //Create 4 new lines in place of previous line
                LineList.push_back(linenew);
                linenew={midpt2,linetemp.endpt,BLUE};
                LineList.push_back(linenew);
                linenew={midpt1,Vector2Add(midpt1,Vector2Rotate(Vector2Subtract(midpt1,linetemp.startpt),-60*DEG2RAD)),BLUE};
                LineList.push_back(linenew);
                linenew={linenew.endpt,midpt2,BLUE};
                LineList.push_back(linenew);
            }
        }
        // cout<<"Deque size="<<LineList.size()<<" Memory:"<<(LineList.size()*sizeof(line))<<endl;

//Draw

        BeginDrawing();
        ClearBackground(BLACK);

        for (uint i=0;i<LineList.size();i++) {
            DrawLineV(LineList[i].startpt,LineList[i].endpt,LineList[i].color);
        }
        if (draw_analysis) {
            DrawCircleLines(500,371,300*1.1547,MAROON);
            float perimeter=3*600*pow(4.0/3.0,levels-1);
            float area_orig=(sqrt(3.0)/4.0)*600.0*600.0;
            float area=(area_orig/5.0)*(8.0-3.0*pow(4.0/9.0,levels-1));
            //cout<<"Perimeter="<<perimeter<<" Area="<<area<<" Area/Perimeter"<<(area/perimeter)<<endl;
            char str[200];
            sprintf(str,"Perimeter=%.0f  Area=%.0f  Area/Perimeter=%.0f",perimeter,area,(area/perimeter));
            DrawText(str,50,800,20,RED);
            float area_limit=2*600*600*sqrt(3.0)/5.0;
            sprintf(str,"Limit of Perimeter = infinity.  Limit of Area=%.0f  Limit of area/perimeter=0",area_limit);
            DrawText(str,50,840,20,RED);
        }

        DrawFPS(10,10);
        EndDrawing();
    }

    return 0;
}