Lsn 10-7
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This document contains a table with x-values from 0 to 360 degrees and a blank column for the corresponding tan(x) values. It also lists four functions - y = -tan(x), y = 2tan(x), y = tan(2x), and y = tan(x)+2 - and indicates they are predictions to be graphed.
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function line(x0, x1, y0, y1)
boolean steep := abs(y1 - y0) > abs(x1 - x0)
if steep then
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swap(x1, y1)
if x0 > x1 then
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real error := 0
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int y := y0
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for x from x0 to x1
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You know that DDA algorithm is an incremental scan conversion method which performs calculations at each step using the results from the preceding step. Here we are going to discover an accurate and efficient raster line generating algorithm, the Bresenham's line-drawing algorithm.
This algorithm was developed by Jack E. Bresenham in 1962 at IBM.
The function given below handles all lines and implements the complete Bresenham's algorithm.
function line(x0, x1, y0, y1)
boolean steep := abs(y1 - y0) > abs(x1 - x0)
if steep then
swap(x0, y0)
swap(x1, y1)
if x0 > x1 then
swap(x0, x1)
swap(y0, y1)
int deltax := x1 - x0
int deltay := abs(y1 - y0)
real error := 0
real deltaerr := deltay / deltax
int y := y0
if y0 < y1 then ystep := 1 else ystep := -1
for x from x0 to x1
if steep then plot(y,x) else plot(x,y)
error := error + deltaerr
if error ? 0.5
y := y + ystep
error := error - 1.0
Boolean alebra
The document provides information about Boolean algebra over 3 paragraphs. It begins with an introduction to Boolean algebra and switching algebra, noting it uses binary logic (1 and 0) to perform mathematical operations. The second paragraph discusses basic logic functions like inverters, OR, and AND gates. The third paragraph explains that Boolean expressions can be implemented as logic circuits, providing an example circuit. The document summarizes key concepts in Boolean algebra in 3 sentences or less.
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2) It provides examples of using these formulas to solve equations such as sin2x + cosx = 0, 2sinxcosx + cosx = 0, and cos2x - sinx = 0.
3) The key steps are to use a double angle formula to get one side equal to zero, factorize the equation, and then solve the resulting trigonometric mini equations.
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Computer graphics - bresenham line drawing algorithm
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Lsn 11-5: Law of Sines
Here are the steps to solve these Law of Sines problems:
1. Given: a = 13, b = 20, A = 75°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(75°)/13 = sin(B)/20
sin(75°)*20/13 = sin(B)
B = sin-1(0.8) = 67°
2. Given: a = 25, B = 38°
Use the Law of Sines: sin(A)/a = sin(B)/b
sin(38°)/25 = sin(m°)/20
sin(38°)*20/25 = sin
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Lsn 10-7
- 2. Graph y = tan(x) on 0 ≤ x ≤ 360 x 30 45 60 90 120 135 150 180 210 225 240 270 300 315 330 360 tan(x) predictions for.... y = tan(x) y = 2tan(x) y = tan(2x) y = tan(x)+2