We are using OpenGL

We have discussed rotation, translation and scaling transformations in class. For this question, we will be using the following notation: R(theta, ax, ay, az) denotes a rotation by theta degrees around the vector (ax, ay, az) * T(dx, dy, dz) denotes a translation by (dx, dy, dz) units, and S(sx, sy, sz) denotes a scaling by (sx, sy, sz) units a) Assume that you have read the coordinates for your letter outline into three float arrays "X[10], Y[10], Z[10" where the initial Z values are zero Describe the sequence of step you would use to transform this geometric model without changing the shape so it is centered at (0,0,0) and the height of the letter (size in Y direction) is 100. Be specific about which of the R, T, S operations you would perform, and how you would calculate the parameters to each of these functions b) What is the formula for translating a point by (dx, dy, dz) units. Show how this can be implemented using a 4x4 matrix multiplication. c) What is the formula for scaling a point by (sx, sy, sz) units. Show how this can be implemented using a 4x4 matrix multiplication. d) Explain with formulas and/or diagrams why you think that order normally matters when you think of a spec order does not matter and ST-TS? We have discussed rotation, translation and scaling transformations in class. For this question, we will be using the following notation: R(theta, ax, ay, az) denotes a rotation by theta degrees around the vector (ax, ay, az) * T(dx, dy, dz) denotes a translation by (dx, dy, dz) units, and S(sx, sy, sz) denotes a scaling by (sx, sy, sz) units a) Assume that you have read the coordinates for your letter outline into three float arrays "X[10], Y[10], Z[10" where the initial Z values are zero Describe the sequence of step you would use to transform this geometric model without changing the shape so it is centered at (0,0,0) and the height of the letter (size in Y direction) is 100. Be specific about which of the R, T, S operations you would perform, and how you would calculate the parameters to each of these functions b) What is the formula for translating a point by (dx, dy, dz) units. Show how this can be implemented using a 4x4 matrix multiplication. c) What is the formula for scaling a point by (sx, sy, sz) units. Show how this can be implemented using a 4x4 matrix multiplication. d) Explain with formulas and/or diagrams why you think that order normally matters when you think of a spec order does not matter and ST-TS