Value for dt ensure no pixels are missed implies dx 1

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Unformatted text preview: rmation Technology - Allahabad DDA Algorithm • • • • x(t ) = x1 + t ( x2 − x1 ) y (t ) = y1 + t ( y2 − y1 ) Start at t = 0 At each step, increment t by dt Choose appropriate value for dt Ensure no pixels are missed: – Implies: dx <1 dt and dx dt dy + dt xnew = xold + ynew = yold dy <1 dt • Set dt to maximum of dx and dy Indian Institute of Information Technology - Allahabad DDA Algorithm The digital differential analyzer (DDA) 0.0 < m ≤ 1.0 ⇒ ∆x = 1 ⇒ yk +1 = yk + m 1 1.0 < m ⇒ ∆y = 1 ⇒ xk +1 = xk + m Equations are based on the assumption that lines are to be processed from the left endpoint to the right endpoint. 0.0 > m ≥ −1.0 ⇒ ∆x = 1 ⇒ yk +1 = yk − m 1 − 1.0 > m ⇒ ∆y = 1 ⇒ xk +1 = xk − m Indian Institute of Information Technology - Allahabad DDA Algorithm #include 'device. h" void lineDDA (int xa, int ya, int xb, int yb) { int dx = xb - xa, dy = yb - ya, steps, k; float xIncrement, yIncrement, x = xa, y = ya; if ( abs(dx) > abs(dy) ) steps = abs (dx) ; else steps = abs (dy); xIncrement = dx / (float) steps; yIncrement = dy / (float) steps; setpixel (ROUNDlxl, ROUND(y) ) : for (k=O; k<steps; k++) { x += xIncrment; y += yIncrement; setpixel (ROUND(x), ROUND(y)); }} 1 Indian Institute of Information Technology - Allahabad DDA algorithm line(int x1, int y1, int x2, int y2) { float x,y; int dx = x2-x1, dy = y2-y1; int n = max(abs(dx),abs(dy)); float dt = n, dxdt = dx/dt, dydt = dy/dt; x = x1; y = y1; while( n-- ) { point(round(x),round(y)); x += dxdt; y += dydt; } } Indian Institute of Information Technology - Allahabad n - range of t. DDA algorithm • Still need a lot of floating point arithmetic. – 2 ‘round’s and 2 adds per pixel. • Is there a simpler way ? • Can we use only integer arithmetic ? – Easier to implement in hardware. Indian Institute of Information Technology - Allahabad Observation on lines. while( n-- ) { draw(x,y); move right; if( below line ) move up; } Indian I...
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