![Line {pt1, pt2, }]is a graphics primitive which represents a line](http://s1.studyres.com/store/data/016208919_1-a4fbe67f9f9c75fe0ecfae82249682ed-300x300.png)
Line {pt1, pt2, }]is a graphics primitive which represents a line
... Line can be used in both Graphics and Graphics3D (two- and three-dimensional graphics). The positions of points can be specified either in absolute coordinates, as {x, y} or {x, y, z}, or in scaled coordinates as Scaled{x, y}] or Scaled{x, y, z}]. The line consists of a sequence of straight segmen ...
... Line can be used in both Graphics and Graphics3D (two- and three-dimensional graphics). The positions of points can be specified either in absolute coordinates, as {x, y} or {x, y, z}, or in scaled coordinates as Scaled{x, y}] or Scaled{x, y, z}]. The line consists of a sequence of straight segmen ...
PDF
... B, so the cubic equation f (x, mx + r) = 0 has two double roots! But this can be remedied, by introducing a second binary operation, +, defined as follows. Let 0 ∈ Cf (R) be any point, and define, for A, B ∈ Cf (R), A + B = 0(AB) . This addition is associative, and in fact, turns Cf (R) into an abel ...
... B, so the cubic equation f (x, mx + r) = 0 has two double roots! But this can be remedied, by introducing a second binary operation, +, defined as follows. Let 0 ∈ Cf (R) be any point, and define, for A, B ∈ Cf (R), A + B = 0(AB) . This addition is associative, and in fact, turns Cf (R) into an abel ...
Linear algebra refresher and transformations
... 3D scene to a 2D pixel coordinate on a camera sensor. • Often we do not care about the depth (“z”) associated with a given (x, y) pixel. So we can remove that row and write as a 3x4 matrix: ...
... 3D scene to a 2D pixel coordinate on a camera sensor. • Often we do not care about the depth (“z”) associated with a given (x, y) pixel. So we can remove that row and write as a 3x4 matrix: ...
The Cartesian plane
... the x-axis, while the vertical line is referred to as the y-axis. The point where the two axes intersect is called the origin. Both axes must be marked (with marks being evenly spaced) y and numbered. The distance between each mark is one unit. ...
... the x-axis, while the vertical line is referred to as the y-axis. The point where the two axes intersect is called the origin. Both axes must be marked (with marks being evenly spaced) y and numbered. The distance between each mark is one unit. ...
Exam No. 01 (Fall 2013) PHYS 320: Electricity and Magnetism I
... 2. (20 points.) A gyroid is an (infinitely connected triply periodic minimal) surface discovered by Alan Schoen in 1970. Schoen presently resides in Carbondale and was a professor at SIU in the later part of his career. Apparently, a gyroid is approximately described by the surface f (x, y, z) = cos ...
... 2. (20 points.) A gyroid is an (infinitely connected triply periodic minimal) surface discovered by Alan Schoen in 1970. Schoen presently resides in Carbondale and was a professor at SIU in the later part of his career. Apparently, a gyroid is approximately described by the surface f (x, y, z) = cos ...
Vector Calculus Operators
... the divergence is greater than zero, it implies a net flux out of a volume element. If the divergence is less than zero, it implies a net flux into a volume element. If the divergence is exactly equal to zero, then there is no net flux into or out of the volume element, i.e., any field lines that en ...
... the divergence is greater than zero, it implies a net flux out of a volume element. If the divergence is less than zero, it implies a net flux into a volume element. If the divergence is exactly equal to zero, then there is no net flux into or out of the volume element, i.e., any field lines that en ...
Number Theory: Elliptic Curves, Problem Sheet 3
... The punchline however is that G(t) := f2 (1, t)2 − 4f1 (1, t)f3 (1, t), which looks like an equation of degree 4 in t, is actually of degree 3 because f2 (0, 1)2 = 4f1 (0, 1)f3 (0, 1). Hence the cubic has now become an equation of the form s2 = G(t) with G a cubic, which is what we were after. 3) An ...
... The punchline however is that G(t) := f2 (1, t)2 − 4f1 (1, t)f3 (1, t), which looks like an equation of degree 4 in t, is actually of degree 3 because f2 (0, 1)2 = 4f1 (0, 1)f3 (0, 1). Hence the cubic has now become an equation of the form s2 = G(t) with G a cubic, which is what we were after. 3) An ...
parametric equations
... Sometimes the equation of a curve is given by expressing the coordinates x and y as functions of a third variable (usually t), called a parameter. Using t as parameter enables us to refer to a particular point on quite complex curves (that we’ve not met so far) ...
... Sometimes the equation of a curve is given by expressing the coordinates x and y as functions of a third variable (usually t), called a parameter. Using t as parameter enables us to refer to a particular point on quite complex curves (that we’ve not met so far) ...
L5-11 Quadratic Systems
... The coordinates of that point are now listed at the bottom. (Round your answer as needed.) ...
... The coordinates of that point are now listed at the bottom. (Round your answer as needed.) ...
1.1 Sets of Real Numbers and The Cartesian Coordinate Plane
... Imagine dropping a vertical line from the x-axis to P and extending a horizontal line from the y-axis to P We describe the point P using the ordered pair (2,-4) ...
... Imagine dropping a vertical line from the x-axis to P and extending a horizontal line from the y-axis to P We describe the point P using the ordered pair (2,-4) ...
Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry. They have the advantage that the coordinates of points, including points at infinity, can be represented using finite coordinates. Formulas involving homogeneous coordinates are often simpler and more symmetric than their Cartesian counterparts. Homogeneous coordinates have a range of applications, including computer graphics and 3D computer vision, where they allow affine transformations and, in general, projective transformations to be easily represented by a matrix.If the homogeneous coordinates of a point are multiplied by a non-zero scalar then the resulting coordinates represent the same point. Since homogeneous coordinates are also given to points at infinity, the number of coordinates required to allow this extension is one more than the dimension of the projective space being considered. For example, two homogeneous coordinates are required to specify a point on the projective line and three homogeneous coordinates are required to specify a point in the projective plane.