If the origin is taken as the centre of projection, then what will be the perspective projection when the projection plane passes through the point P(4;5;3) and has normal vector (1;2;-1).
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If the origin is taken as the centre of projection, then what will be the perspective projection when the projection plane passes through the point P(4;5;3) and has normal
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- Please note that neither the center of projection nor the projection plane is at the origin. So please use the appropriate general perspective projection matrix to solve this problem. I have attached an image of the projection matrix that you have to use where Qdx is the x coordinate of the center of projection, Qdy is the y coordinate of the center of projection, and zp is the z coordinate of the center of the projection plane. 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.This is a Computer Graphics Question on Linear Transformation. Please show all steps of the derivation. Derive |4x4| rotation matrix for a 3D point rotation across Z-axis and the center of rotation is (a, b, c).Computer Graphics Develop an algorithm for calculating the normal vector to a Bezier surfaces at the point P(u, v).
- Let v be a vector whose coordinates are given as v = [vx, Vy, Vz. If the quaternion Q represents a rotation, show that the new, rotated coordinates of v are given by Q(0, Vx, Vy, Vz)Q*, where (0, vx, Vy, Vz) is a quaternion with zero as its real component.Given two squares on a two-dimensional plane, find a line that would cut these twosquares in half. Assume that the top and the bottom sides of the square run parallel to the x-axis5. The derivative is the gradient of the tangent to the function. In the case of a semi-circle, this means that the gradient vector (1, dy/d.r) should be orthogonal to the vector(arn, Y0). Verify this using the dot product and also by plotting both vectors (normalise the gradient vector).
- Perform scaling on a triangle (1, 1), (8, 1) and (1, 9) with a scaling factor of 2 in both x y-directions. Find the final coordinates and of the triangle.This is a Computer Graphics Question on Phong's Lighting Model. Question: A light source with intensity 50 and radius of influence 100 is located at (4,2,93) from which you are called to calculate the illumination of a point on the yz plane. For no shiny surface and negligible ambient light, find the point on the surface with the highest illumination and light intensity at that point. Given the diffuse coefficient is 0.7.Explain Bresenham line draw algorithm. calculate the coordinate of the point on the line by using Bresenham line algorithm from (7, 8) to (22, 19).
- Determine if the vector is a gradient and if it is, find a function having the given vector as its gradient. 2xyi + (1+x²) j = 0Bu = ƒ and Cu = f might be solvable even though B and C are singular. Show that every vector f = Bu has ƒ1 + ƒ2+ ……. +fn = 0. Physical meaning: the external forces balance. Linear algebra meaning: Bu = ƒ is solvable when ƒ is perpendicular to the all – ones column vector e = (1, 1, 1, 1…) = ones (n, 1).Consider a rectangle with perimeter 28 (units). Let the width of the rectangle be w (units) and let the Area of the region enclossed by the rectangle be A (square units). Express A as a function of w and state the domain of the function.