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Q5. Show the values of the decision function and the pixels selected by the Bresenham line algorithm for the line from (1, 2) to (8, 12). Bresenham's Line Algorithm for $|m| < 1$ 1. Input the two endpoints and store the left endpoint in $(x_0, y_0)$. 2. Load $(x_0, y_0)$ into the frame buffer; i.e., plot the first point. 3. Calculate the constants $dx$, $dy$, $2dy$, and $2dy - 2dx$, and obtain the starting value for the decision function $d_0 = 2dy - dx$. 4. At each $x_k$ along the line, starting at $k = 0$, perform the following test: If $d_k < 0$, the next point to plot is $(x_k + 1, y_k)$ and $d_{k+1} = d_k + 2\Delta y$. Otherwise the next point to plot is $(x_k + 1, y_k + 1)$ and $d_{k+1} = d_k + 2(\Delta y - \Delta x)$. 5. Repeat step 4 $\Delta x$ times. $d = 2(\Delta y) - (\Delta x)$ • Initial value $2(\Delta y) - (\Delta x)$ • Case 1: $d \leftarrow d + \Delta_E$, where $\Delta_E = 2(\Delta y)$ • Case 2: $d \leftarrow d + \Delta_{NE}$ where $\Delta_{NE} = 2\{(\Delta y) - (\Delta x)\}$

          Q5. Show the values of the decision function and the pixels selected by the Bresenham line
algorithm for the line from (1, 2) to (8, 12).
Bresenham's Line Algorithm for $|m| < 1$
1. Input the two endpoints and store the left endpoint in $(x_0, y_0)$.
2. Load $(x_0, y_0)$ into the frame buffer; i.e., plot the first point.
3. Calculate the constants $dx$, $dy$, $2dy$, and $2dy - 2dx$, and
obtain the starting value for the decision function $d_0 = 2dy - dx$.
4. At each $x_k$ along the line, starting at $k = 0$, perform the
following test:
If $d_k < 0$, the next point to plot is $(x_k + 1, y_k)$ and $d_{k+1} = d_k + 2\Delta y$.
Otherwise the next point to plot is $(x_k + 1, y_k + 1)$ and
$d_{k+1} = d_k + 2(\Delta y - \Delta x)$.
5. Repeat step 4 $\Delta x$ times.
$d = 2(\Delta y) - (\Delta x)$
• Initial value $2(\Delta y) - (\Delta x)$
• Case 1: $d \leftarrow d + \Delta_E$, where $\Delta_E = 2(\Delta y)$
• Case 2: $d \leftarrow d + \Delta_{NE}$
where $\Delta_{NE} = 2\{(\Delta y) - (\Delta x)\}$

Q5. Show the values of the decision function and the pixels selected by the Bresenham line
algorithm for the line from (1, 2) to (8, 12).
Bresenham's Line Algorithm for |m| < 1
1. Input the two endpoints and store the left endpoint in (x0, y0).
2. Load (x0, y0) into the frame buffer; i.e., plot the first point.
3. Calculate the constants dx, dy, 2dy, and 2dy - 2dx, and
obtain the starting value for the decision function d0 = 2dy - dx.
4. At each xk along the line, starting at k = 0, perform the
following test:
If dk < 0, the next point to plot is (xk + 1, yk) and dk+1 = dk + 2Δ y.
Otherwise the next point to plot is (xk + 1, yk + 1) and
dk+1 = dk + 2(Δ y - Δ x).
5. Repeat step 4 Δ x times.
d = 2(Δ y) - (Δ x)
• Initial value 2(Δ y) - (Δ x)
• Case 1: d ← d +, where = 2(Δ y)
• Case 2: d ← d + ΔNE
where ΔNE = 2{(Δ y) - (Δ x)}

Added by Teresa S.

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