Написание документации: кватернионы и версоры

docs/versor-eng.md

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+# Versors
+
+Quaternions are complex numbers which have one real component and three
+imaginary components.
+
+A quaternion can be viewed as a four-dimensional vector:
+
+1. summation and subtraction of quaternions are same as for four-dimensional
+vectors in Euclidean space;
+
+2. quaternions can be multiplied by real numbers the same way as
+four-dimensional vectors;
+
+3. the modulus of a quaternion is calculated in exactly the same way as
+the modulus of a vector in four-dimensional Euclidean space;
+
+4. the multiplication of two quaternions can be represented as the product
+of a 4x4 matrix and a four-dimensional vector.
+
+A quaternion has four degrees of freedom. But if we introduce a constraint in
+the form of a requirement that the modulus of this quaternion be equal to one,
+then such a set of quaternions will have only three degrees of freedom.
+
+These quaternions represent a sphere of radius 1 in four-dimensional space.
+The "surface" of this sphere has a dimension equal to three.
+
+Quaternions of unit length describe rotations in three-dimensional space very
+well. And this is logical, because rotations in three-dimensional space have
+three degrees of freedom, just like a sphere in four-dimensional space.
+
+There is a special name for a quaternion of unit length: versor.
+
+Versors are quaternions of unit length.
+
+## Implementation of versors in the library
+
+The library has a separate implementation for versors in the form of special
+structures and a set of functions that keep the modulus of a versorclose to one.
+
+There are two structures for versors: **BgFP32Versor** and **BgFP64Versor**:
+
+    typedef struct {
+        const float s0, x1, x2, x3;
+    } BgFP32Versor;
+
+    typedef struct {
+        const double s0, x1, x2, x3;
+    } BgFP64Versor;
+
+The fields are deliberately declared const so that a developer using these
+structures is not tempted to change the values ​​of the fields directly.
+
+With these structures, it is better to use special functions that allow you
+to save new values ​​in the structure fields of **BgFP32Versor** and
+**BgFP64Versor**.