Line drawing algorithm
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The document describes two algorithms for drawing lines on a graph: 1. The DDA (Digital Differential Analyzer) line drawing algorithm which calculates the slope of the line and uses incremental steps to determine each new pixel coordinate. 2. Bresenham's line drawing algorithm which uses a decision parameter to determine whether the next pixel is directly above/below or diagonal to the current pixel in order to draw lines with integer coordinates.
Line drawing algorithm
- 1. DDA line drawing algorithm Stage 1: Read the contribution of the end purposes of the line as (x1,y1) and (x2,y2) with the end goal that x1!=x2 and y1!=y2 Stage 2: Calculate dx=x2-x1 and dy=y2-y1 Stage 3: if(dx>=dy) step=dx else step=dy Stage 4: xin=dx/step and yin=dy/step Stage 5: x=x1+0.5 and y=y1+0.5 Stage 6: for(k=0;k<step;k++) { X=x+xin; Y=y+yin; Putpixel(x,y); } C program for DDA #include<stdio.h> #include<conio.h> #include<math.h> #include<dos.h> #include<graphics.h> void main() { float x,y,x1,y1,x2,y2,dx,dy,step; int i, gd=DETECT,gm; initgraph(&gd,&gm,"c:tcbgi");
- 2. printf("Enter the starting coordinates"); scanf("%f%f",&x1,&y1); printf("Enter the ending coordinates"); scanf("%f%f",&x2,&y2); dx=abs(x2-x1); dy=abs(y2-y1); if(dx>=dy) step=dx; else step=dy; dx=dx/step; dy=dy/step; x=x1; y=y1; i=1; while(i<=step) { putpixel(x,y,5); x=x+dx; y=y+dx; i=i+1; delay(100); } getch(); closegraph(); }
- 3. Bresenham’s line drawing algorithm Step 1: Start. Step 2: Now, we consider Starting point as (x1, y1) and ending point (x2, y2). Step 3: Now, we have to calculate dx and dy. dx = x2-x1 dy = y2-y1 m = dy/dx Step 4: Now, we will calculate the decision parameter pk with following formula. pk = 2dy-dx Step 5: The initial coordinates of the line are (xk, yk), and the next coordinates are (xk+1, yk+1). Now, we are going to calculate two cases for decision parameter pk Case 1: If pk < 0 Then pk+1 =pk +2dy xk+1 = xk +1 yk+1 = yk Case 2: If pk >= 0 Then pk+1 =pk +2dy-2dx xk+1 =xk +1 yk+1 =yk +1 Step 6: We will repeat step 5 until we found the ending point of the line and the total number of iterations =dx-1. Step 7: Stop.
- 4. C program to implement Bresenham’s line drawing # include <stdio.h> # include <conio.h> # include <graphics.h> int main() { int dx,dy,x,y,p,x1,y1,x2,y2; int gd,gm; printf("nntEnter the co-ordinates of first point : "); scanf("%d %d",&x1,&y1); printf("nntEnter the co-ordinates of second point : "); scanf("%d %d",&x2,&y2); dx = (x2 - x1); dy = (y2 - y1); p = 2 * (dy) - (dx); x = x1; y = y1; detectgraph(&gd,&gm); initgraph(&gd,&gm,"c:tcbgi"); putpixel(x,y,WHITE); while(x <= x2) { if(p < 0) { x=x+1; y=y; p = p + 2 * (dy); }
- 5. else { x=x+1; y=y+1; p = p + 2 * (dy - dx); } putpixel(x,y,WHITE); } getch(); closegraph(); }