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  2. Rotations and reflections in two dimensions - Wikipedia

    en.wikipedia.org/wiki/Rotations_and_reflections...

    Let a rotation about the origin O by an angle θ be denoted as Rot(θ). Let a reflection about a line L through the origin which makes an angle θ with the x-axis be denoted as Ref(θ). Let these rotations and reflections operate on all points on the plane, and let these points be represented by position vectors.

  3. Point reflection - Wikipedia

    en.wikipedia.org/wiki/Point_reflection

    In mathematics, reflection through the origin refers to the point reflection of Euclidean space R n across the origin of the Cartesian coordinate system. Reflection through the origin is an orthogonal transformation corresponding to scalar multiplication by − 1 {\displaystyle -1} , and can also be written as − I {\displaystyle -I} , where I ...

  4. Reflection (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Reflection_(mathematics)

    Point Q is the reflection of point P through the line AB. In a plane (or, respectively, 3-dimensional) geometry, to find the reflection of a point drop a perpendicular from the point to the line (plane) used for reflection, and extend it the same distance on the other side. To find the reflection of a figure, reflect each point in the figure.

  5. Euclidean plane isometry - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane_isometry

    (F is for "flip".) have the effect of reflecting the point p in the line L that is perpendicular to v and that passes through c. The line L is called the reflection axis or the associated mirror. To find a formula for F c,v, we first use the dot product to find the component t of p − c in the v direction,

  6. Plane-based geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Plane-based_geometric_algebra

    In the plane-based geometric algebra notation, this rotoreflection can be thought of as a planar reflection "added to" a point reflection. The plane part of this rotoreflection is the plane that is orthogonal to the line L and the original point P. A similar procedure can be used to find the line orthogonal to a plane and passing through a ...

  7. Bidirectional reflectance distribution function - Wikipedia

    en.wikipedia.org/wiki/Bidirectional_reflectance...

    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 ...

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    www.aol.com/lifestyle/we-found-14-personalized...

    Personalized gifts don't have to be expensive or purchased months in advance. Give a thoughtful gift from Walmart this year, starting at just $5.

  9. Vincenty's formulae - Wikipedia

    en.wikipedia.org/wiki/Vincenty's_formulae

    longitude of the points; L = L 2 − L 1: difference in longitude of two points; λ: Difference in longitude of the points on the auxiliary sphere; α 1, α 2: forward azimuths at the points; α: forward azimuth of the geodesic at the equator, if it were extended that far; s: ellipsoidal distance between the two points; σ: angular separation ...