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The Schwarz function of a curve in the complex plane is an analytic function which maps the points of the curve to their complex conjugates.It can be used to generalize the Schwarz reflection principle to reflection across arbitrary analytic curves, not just across the real axis.
In the complex reflection coefficient plane the Smith chart occupies a circle of unity radius centred at the origin. In cartesian coordinates therefore the circle would pass through the points (+1,0) and (−1,0) on the x-axis and the points (0,+1) and (0,−1) on the y-axis.
A reflection through an axis. In mathematics, a reflection (also spelled reflexion) [1] is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as the set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflection. The image of a figure by a reflection is its mirror image in ...
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Diagram showing vectors used to define the BRDF. All vectors are unit length. points toward the light source. points toward the viewer (camera). is the surface normal.. The bidirectional reflectance distribution function (BRDF), symbol (,), is a function of four real variables that defines how light from a source is reflected off an opaque surface. It is employed in the optics of real-world ...
An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and ...
Parts of this Wikipedia page (those related to including information about native vega support via the graph extension) need to be updated. Please help update this Wikipedia page to reflect recent events or newly available information. Relevant discussion may be found on the talk page. (January 2015)
Then the xz plane is the interface, and the y axis is normal to the interface (see diagram). Let i and j (in bold roman type) be the unit vectors in the x and y directions, respectively. Let the plane of incidence be the xy plane (the plane of the page), with the angle of incidence θ i measured from j towards i.