Q9) To store/represent a 3D sphere as model-based computer graphics object in my computer I need a minimum of • 3 variables • 2 variables • 4 variables • 1 variable Q10) x(t) = a Cos(t) + cx Y (t) = b Sin(t) + cy For the above ellipse paramteric equation; If l want to flip 90 degrees around (cx, cy), I should have a. x(t) = Cos{t) + cx Y(t) = b Sin(t) cy b. X(t) = b Cos(t) + cx Y (t) = a Sin(t) cy c. X(t) = a Cos(t): cy Y(t) = b Sin(t) + cX d. Y(t) = a Cos(t) + cx x(t) = b Sin(t) + cy
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- What role does the reflection vector play in computer graphics? The following should have at least two examples of each.The compass gradient operators of size 3x3 are designed to measure gradients of edges oriented in eight directions: E, NE, N, NW, W, SW, S, and SE. i) Give the form of these eight operators using coefficients valued 0, 1 or – 1. ii) Specify the gradient vector direction of each mask, keeping in mind that the gradient direction is orthogonal to the edge direction.Lesson: Application of Computer Graphics Given an orthographic camera with direction d, up u, and center c properties (size is fixed to 1), show the formula for generating a ray for point (x, y) in the screen (0,0 <= x, y <= 1,1). Remember, a ray has an origin and a direction.
- This problem is on Computer Graphics and is based on the topic 'Perspective Projection'. Please provide a step-by-step solution to the problem and explain the steps. The solution must include the General purpose perspective projection matrix. Question: Let a 3D point (423, -423, 423) be projected on a projection plane. Given that the center of the projection plane is (0.0, 0.0, -423.0) and the coordinate of the COP is (4, 2, 3). Determine the coordinate of that 3D point on the projection plane using a general purpose perspective projection matrix.Computer Science Let C be a black circular disk in front of a white background. The circular disk is parallel to the image plane. This disk is projected on the image plane through a pinhole. What is the shape of the disk’s projection on the image plane? [Hint: A circular disk parallel to the image plane is described algebraically as all 3D points [X,Y,Z]T with (X-X0) 2 +(Y-Y0) 2 =R2 , Z=Z0, where [X0,Y0,Z0] T is the center of the disk and R is its radius.]5. Lemniscate or figure 8 You should have learned lemniscate or the famous figure 8 in high school as well. The following is a snip from Wikipedia. Lemniscate of Bernoulli From Wikipedia, the free encyclopedia In geometry, the lemniscate of Bernoulli is a plane curve defined from two given points F1 and F2, known as foci, at distance 2c from each other as the locus of points P so that PF₁·PF₂ = c². The curve has a shape similar to the numeral 8 and to the ∞ symbol. Its name is F2 P A lemniscate of Bernoulli and its two foci F₁ and F2 Figure 8. Write a computer program (with graphics and GUI parts) that draws the figure 8. Show your analysis if applicable (which means any equation?). 9
- 5. F has one-tó-one correspondence. F {(-5, p), (10, w), (15, n), (20, m), (25, u), (30, b)}. Draw an arrow diagram for F. %3DWhat is the function of the reflection vector in computer graphics? Each of the following should have at least two examples.Q. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it. .
- Q1. Given a 2d grid map of '1's (land) and '0's (water),count the number of islands.An island is surrounded by water and is formed byconnecting adjacent lands horizontally or vertically.You may assume all four edges of the grid are all surrounded by water. Example 1: 11110110101100000000Answer: 1 Example 2: 11000110000010000011Answer: 3""" def num_islands(grid): count = 0 for i in range(len(grid)): for j, col in enumerate(grid[i]): if col == 1: dfs(grid, i, j) count += 1 Please code it.Given A={1,2,3,4,56}, B= {2,4,5,6} and C= (1,6,7} 1. B' U C'=What does the following lambda expression compute: λ(x)x × x × x