Исправление существовавших и добавление новых функций сравнения

README-Eng.md

@@ -1,6 +1,6 @@
-# Basic Geometry
+# Basic Geometry Computations
 
-## Library of basic geometric computations
+## Library of basic geometric computations for C
 
 [Версия на русском языке / Russian version](./README.md)
 

README.md

@@ -1,6 +1,6 @@
-# Basic Geometry
+# Basic Geometry Computations
 
-## Библиотека базовых геометрических вычислений
+## Библиотека базовых геометрических вычислений для Си
 
 (English: library of basic geometric computations)
 
@@ -36,5 +36,5 @@
 типа **float**, а другая - для данных типа **double**. Но между этими половинами
 есть мостики - функции преобразования типа.
 
-Однако в библиотеке нет функций, которые используют для вычисления данные разных
-типов (**float** и *double* одновременно).
+Однако в библиотеке мало функций, которые используют для вычисления данные разных
+типов (**float** и **double** одновременно).

basic-geometry/quaternion.c

@@ -59,3 +59,6 @@ extern inline void bgc_quaternion_divide_fp64(const BgcQuaternionFP64* dividend,
 
 extern inline void bgc_quaternion_get_product_fp32(const BgcQuaternionFP32* left, const BgcQuaternionFP32* right, BgcQuaternionFP32* product);
 extern inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const BgcQuaternionFP64* right, BgcQuaternionFP64* product);
+
+extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);
+extern inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2);

basic-geometry/quaternion.h

@@ -535,4 +535,42 @@ inline void bgc_quaternion_get_product_fp64(const BgcQuaternionFP64* left, const
     product->x3 = x3;
 }
 
+// ================== Are Close ================= //
+
+inline int bgc_quaternion_are_close_fp32(const BgcQuaternionFP32* quaternion1, const BgcQuaternionFP32* quaternion2)
+{
+    const float ds0 = quaternion1->s0 - quaternion2->s0;
+    const float dx1 = quaternion1->x1 - quaternion2->x1;
+    const float dx2 = quaternion1->x2 - quaternion2->x2;
+    const float dx3 = quaternion1->x3 - quaternion2->x3;
+
+    const float square_modulus1 = bgc_quaternion_get_square_modulus_fp32(quaternion1);
+    const float square_modulus2 = bgc_quaternion_get_square_modulus_fp32(quaternion2);
+    const float square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);
+
+    if (square_modulus1 <= BGC_EPSYLON_EFFECTIVENESS_LIMIT_FP32 || square_modulus2 <= BGC_EPSYLON_EFFECTIVENESS_LIMIT_FP32) {
+        return square_distance <= BGC_SQUARE_EPSYLON_FP32;
+    }
+
+    return square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP32 * square_modulus2;
+}
+
+inline int bgc_quaternion_are_close_fp64(const BgcQuaternionFP64* quaternion1, const BgcQuaternionFP64* quaternion2)
+{
+    const double ds0 = quaternion1->s0 - quaternion2->s0;
+    const double dx1 = quaternion1->x1 - quaternion2->x1;
+    const double dx2 = quaternion1->x2 - quaternion2->x2;
+    const double dx3 = quaternion1->x3 - quaternion2->x3;
+
+    const double square_modulus1 = bgc_quaternion_get_square_modulus_fp64(quaternion1);
+    const double square_modulus2 = bgc_quaternion_get_square_modulus_fp64(quaternion2);
+    const double square_distance = (ds0 * ds0 + dx1 * dx1) + (dx2 * dx2 + dx3 * dx3);
+
+    if (square_modulus1 <= BGC_EPSYLON_EFFECTIVENESS_LIMIT_FP64 || square_modulus2 <= BGC_EPSYLON_EFFECTIVENESS_LIMIT_FP64) {
+        return square_distance <= BGC_SQUARE_EPSYLON_FP64;
+    }
+
+    return square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus1 && square_distance <= BGC_SQUARE_EPSYLON_FP64 * square_modulus2;
+}
+
 #endif // _BGC_QUATERNION_H_

basic-geometry/tangent.c

@@ -46,6 +46,9 @@ extern inline void bgc_tangent_turn_vector_fp64(const BgcTangentFP64* tangent, c
 extern inline void bgc_tangent_turn_vector_back_fp32(const BgcTangentFP32* tangent, const BgcVector2FP32* vector, BgcVector2FP32* result);
 extern inline void bgc_tangent_turn_vector_back_fp64(const BgcTangentFP64* tangent, const BgcVector2FP64* vector, BgcVector2FP64* result);
 
+extern inline int bgc_tangent_are_close_fp32(const BgcTangentFP32* tangent1, const BgcTangentFP32* tangent2);
+extern inline int bgc_tangent_are_close_fp64(const BgcTangentFP64* tangent1, const BgcTangentFP64* tangent2);
+
 void _bgc_tangent_normalize_fp32(const float square_modulus, _BgcDarkTwinTangentFP32* twin)
 {
     // (square_modulus != square_modulus) is true when square_modulus is NaN

basic-geometry/tangent.h

@@ -343,4 +343,22 @@ inline void bgc_tangent_turn_vector_back_fp64(const BgcTangentFP64* tangent, con
     result->x2 = x2;
 }
 
+// ================== Are Close ================= //
+