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  2. 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 ...

  3. Alhazen's problem - Wikipedia

    en.wikipedia.org/wiki/Alhazen's_problem

    They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six. [15] Alhazen's problem can also be extended to multiple refractions from a spherical ball.

  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. Rotations and reflections in two dimensions - Wikipedia

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

    The set of all reflections in lines through the origin and rotations about the origin, together with the operation of composition of reflections and rotations, forms a group. The group has an identity: Rot(0). Every rotation Rot(φ) has an inverse Rot(−φ). Every reflection Ref(θ) is its own inverse. Composition has closure and is ...

  6. Plane-based geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Plane-based_geometric_algebra

    L is a 2-reflection and is a 3-reflection, so taking their geometric product PL in some sense produces a 5-reflection; however, as in the picture below, two of these reflections cancel, leaving a 3-reflection (sometimes known as a rotoreflection). In the plane-based geometric algebra notation, this rotoreflection can be thought of as a planar ...

  7. Transformation matrix - Wikipedia

    en.wikipedia.org/wiki/Transformation_matrix

    A reflection about a line or plane that does not go through the origin is not a linear transformation — it is an affine transformation — as a 4×4 affine transformation matrix, it can be expressed as follows (assuming the normal is a unit vector): [′ ′ ′] = [] [] where = for some point on the plane, or equivalently, + + + =.

  8. Step potential - Wikipedia

    en.wikipedia.org/wiki/Step_potential

    To find the amplitudes for reflection and transmission for incidence from the left, we set in the above equations A → = 1 (incoming particle), A ← = √ R (reflection), B ← = 0 (no incoming particle from the right) and B → = √ Tk 1 /k 2 (transmission [1]). We then solve for T and R. The result is:

  9. Rotation matrix - Wikipedia

    en.wikipedia.org/wiki/Rotation_matrix

    rotates points in the xy plane counterclockwise through an angle θ about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates v = (x, y), it should be written as a column vector, and multiplied by the matrix R: