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What is the value of the initial decision parameter p0 in Bresenham's line drawing algorithm?
What is the value of the y-intercept b in the line equation $y = mx + b$?
What is the value of the slope m in the line equation $y = mx + b$?
In Bresenham's line drawing algorithm, how is the next pixel to plot determined if the decision parameter p_k is less than 0?
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In Bresenham's line drawing algorithm, how is the next pixel to plot determined if the decision parameter p_k is greater than or equal to 0?
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What is the value of the constant 2Δy - 2Δx used in Bresenham's line drawing algorithm?
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What is the value of the constant 2Δy used in Bresenham's line drawing algorithm?
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For the line with endpoints (20, 10) and (30, 18), what is the value of Δx?
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For the line with endpoints (20, 10) and (30, 18), what is the value of Δy?
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For the line with endpoints (20, 10) and (30, 18), what is the value of the initial decision parameter p0?
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For the line with endpoints (20, 10) and (30, 18), what is the value of the slope m?
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Study Notes
Bresenham's Line Algorithm
- Bresenham's Line Algorithm is an efficient raster line-generating algorithm that uses only incremental integer calculations.
- It is used for scan-converting lines with positive slope less than 1.0.
Calculating Pixel Separations
- At sampling position xk + 1, the y-coordinate on the mathematical line is calculated as y = m(xk + 1) + b.
- The vertical pixel separations from the mathematical line path are labeled as dlower and dupper.
- dlower = y - yk = m(xk + 1) + b - yk and dupper = (yk + 1) - y = (yk + 1) - m(xk + 1) - b.
Determining the Closest Pixel
- The difference between the two pixel separations is calculated as dlower - dupper = 2m(xk + 1) - 2yk + 2b - 1.
- The decision parameter pk is set up to determine which pixel is closest to the line path.
- pk = 2∆y * xk - 2∆x * yk + 2∆y + ∆x(2b - 1) = 2∆y * xk - 2∆x * yk + C.
- If pk is negative, the pixel at yk is "closer" to the line path, and the lower pixel is plotted; otherwise, the upper pixel is plotted.
Incremental Integer Calculations
- The decision parameter pk is calculated using incremental integer calculations.
- The sign of pk is the same as the sign of dlower - dupper.
- The values of successive decision parameters are obtained using incremental integer calculations.
- pk+1 = pk + 2∆y - 2∆x(yk+1 - yk).
Bresenham's Line-Drawing Algorithm
- The algorithm is used for |m| < 1.0.
- The steps involved in the algorithm are:
- Input the two line endpoints and store the left endpoint in (x0, y0).
- Set the color for frame-buffer position (x0, y0) and plot the first point.
- Calculate the constants ∆x, ∆y, 2∆y, and 2∆y - 2∆x, and obtain the starting value for the decision parameter as p0 = 2∆y - ∆x.
- At each xk along the line, starting at k = 0, perform the following test. If pk < 0, the next point to plot is (xk + 1, yk) and pk+1 = pk + 2∆y. Otherwise, the next point to plot is (xk + 1, yk + 1) and pk+1 = pk + 2∆y - 2∆x.
- Perform step 4 ∆x - 1 times.
Example
- For the line (x0, y0) = (20, 10) and (xend, yend) = (30, 18), the line has a slope of 0.8, ∆x = 10, and ∆y = 8.
- The initial decision parameter p0 = 2∆y - ∆x = 6.
- The increments for calculating successive decision parameters are 2∆y = 16 and 2∆y - 2∆x = -4.
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Description
Test your understanding of Bresenham's Line Algorithm, an efficient raster line-generating algorithm that uses incremental integer calculations. This quiz focuses on the scan-conversion process for lines with positive slope less than 1.0 and the decision-making process for plotting pixels.
