homogenous-transformation

When using the Scala standard lib, I can do somthing like this: scala> val scalaList = List(1,2,3) scalaList: List[Int] = List(1, 2, 3) scala> scalaList.foldLeft(0)((acc,n)=>acc+n) res0: Int = 6 Making one Int out of many Ints. And I can do something like this: scala> scalaList.foldLeft("")((acc,n)=>acc+n.toString) res1: String = 123 Making one String out of many Ints. So, foldLeft could be either homogeneous or heterogeneous, whichever we want, it's in one API. While in Spark, if I want one Int out of many Ints, I can do this: scala> val rdd = sc.parallelize(List(1,2,3)) rdd: org.apache.spark

I am given the locations of three points: p1 = [1.0, 1.0, 1.0] p2 = [1.0, 2.0, 1.0] p3 = [1.0, 1.0, 2.0] and their transformed counterparts: p1_prime = [2.414213562373094, 5.732050807568877, 0.7320508075688767] p2_prime = [2.7677669529663684, 6.665063509461097, 0.6650635094610956] p3_prime = [2.7677669529663675, 5.665063509461096, 1.6650635094610962] The affine transformation matrix is of the form trans_mat = np.array([[…, …, …, …], […, …, …, …], […, …, …, …], […, …, …, …]]) such that with import numpy as np def transform_pt(point, trans_mat): a = np.array([point[0], point[1], point[2], 1]) ap

how do we extract scale matrix from model view matrix? Right now I am taking length of each coloumn, but it fails when the scale is negative. here is my code: float xs = matrix[0][0] * matrix[0][1] * matrix[0][2] * matrix[0][3] < 0 ? -1 : 1; float ys = matrix[1][0] * matrix[1][1] * matrix[1][2] * matrix[1][3] < 0 ? -1 : 1; float zs = matrix[2][0] * matrix[2][1] * matrix[2][2] * matrix[2][3] < 0 ? -1 : 1; glm::vec3 new_scale; new_scale.x = xs* glm::sqrt( matrix[0][0] * matrix[0][0] + matrix[0][1] * matrix[0][1] + matrix[0][2] * matrix[0][2]); new_scale.y = ys* glm::sqrt( matrix[1][0] * matrix[1

I want to do some 2D drawing and thus want to implement some matrix transformations. With my light mathematics background I am trying to understand how to do so in C# (any other oop language would do it obviously). All I read is explaining that we need to work with 3x3 matrices to be able to cope with the translations. Because you cannot make translation with multiplications. But this is with multiplications of the matrices that we create our transformations. So we work with something like: { x1, x2, tx } { y1, y2, ty } { 0, 0, 1 } I understand the mean of the third column, but why do we need