Добавлены функции возведения в степень, экспоненты и логарифма для дуальных чисел, добавлены функции магнитуды для дуальных кватернионов

basic-geometry/dual-number.c

@@ -71,3 +71,12 @@ extern inline void bgc_fp64_dual_number_get_mean3(BGC_FP64_DualNumber* const mea
 
 extern inline void bgc_fp32_dual_number_interpolate(BGC_FP32_DualNumber* const interpolation, const BGC_FP32_DualNumber* const first, const BGC_FP32_DualNumber* const second, const float phase);
 extern inline void bgc_fp64_dual_number_interpolate(BGC_FP64_DualNumber* const interpolation, const BGC_FP64_DualNumber* const first, const BGC_FP64_DualNumber* const second, const double phase);
+
+extern inline void bgc_fp32_dual_number_power(BGC_FP32_DualNumber* const power, const BGC_FP32_DualNumber* const number, const float degree);
+extern inline void bgc_fp64_dual_number_power(BGC_FP64_DualNumber* const power, const BGC_FP64_DualNumber* const number, const double degree);
+
+extern inline void bgc_fp32_dual_number_exponent(BGC_FP32_DualNumber* const exponent, const BGC_FP32_DualNumber* const degree);
+extern inline void bgc_fp64_dual_number_exponent(BGC_FP64_DualNumber* const exponent, const BGC_FP64_DualNumber* const degree);
+
+extern inline int bgc_fp32_dual_number_ln(BGC_FP32_DualNumber* const logarithm, const BGC_FP32_DualNumber* const number);
+extern inline int bgc_fp64_dual_number_ln(BGC_FP64_DualNumber* const logarithm, const BGC_FP64_DualNumber* const number);

basic-geometry/dual-number.h

@@ -448,4 +448,62 @@ inline void bgc_fp64_dual_number_interpolate(BGC_FP64_DualNumber* const interpol
     interpolation->dual_part = first->dual_part * counter_phase + second->dual_part * phase;
 }
 
+// =================== Power ==================== //
+
+inline void bgc_fp32_dual_number_power(BGC_FP32_DualNumber* const power, const BGC_FP32_DualNumber* const number, const float degree)
+{
+    const float base = powf(number->real_part, degree - 1.0f);
+
+    power->real_part = base * number->real_part;
+    power->dual_part = base * number->dual_part * degree;
+}
+
+inline void bgc_fp64_dual_number_power(BGC_FP64_DualNumber* const power, const BGC_FP64_DualNumber* const number, const double degree)
+{
+    const double base = pow(number->real_part, degree - 1.0);
+
+    power->real_part = base * number->real_part;
+    power->dual_part = base * number->dual_part * degree;
+}
+
+// ================== Exponent ================== //
+
+inline void bgc_fp32_dual_number_exponent(BGC_FP32_DualNumber* const exponent, const BGC_FP32_DualNumber* const degree)
+{
+    exponent->real_part = expf(degree->real_part);
+    exponent->dual_part = exponent->real_part * degree->dual_part;
+}
+
+inline void bgc_fp64_dual_number_exponent(BGC_FP64_DualNumber* const exponent, const BGC_FP64_DualNumber* const degree)
+{
+    exponent->real_part = exp(degree->real_part);
+    exponent->dual_part = exponent->real_part * degree->dual_part;
+}
+
+// ============= Natural Logarithm ============== //
+
+inline int bgc_fp32_dual_number_ln(BGC_FP32_DualNumber* const logarithm, const BGC_FP32_DualNumber* const number)
+{
+    if (number->real_part <= 0.0f) {
+        return BGC_FAILURE;
+    }
+
+    logarithm->real_part = logf(number->real_part);
+    logarithm->dual_part = logarithm->real_part * number->dual_part / number->real_part;
+
+    return BGC_SUCCESS;
+}
+
+inline int bgc_fp64_dual_number_ln(BGC_FP64_DualNumber* const logarithm, const BGC_FP64_DualNumber* const number)
+{
+    if (number->real_part <= 0.0) {
+        return BGC_FAILURE;
+    }
+
+    logarithm->real_part = log(number->real_part);
+    logarithm->dual_part = logarithm->real_part * number->dual_part / number->real_part;
+
+    return BGC_SUCCESS;
+}
+
 #endif

basic-geometry/dual-quaternion.c

@@ -3,6 +3,12 @@
 extern inline void bgc_fp32_dual_quaternion_reset(BGC_FP32_DualQuaternion* const quaternion);
 extern inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* const quaternion);
 
+extern inline void bgc_fp32_dual_quaternion_get_square_magnitude(BGC_FP32_DualNumber* const square_magnitude, const BGC_FP32_DualQuaternion* const quaternion);
+extern inline void bgc_fp64_dual_quaternion_get_square_magnitude(BGC_FP64_DualNumber* const square_magnitude, const BGC_FP64_DualQuaternion* const quaternion);
+
+extern inline void bgc_fp32_dual_quaternion_get_magnitude(BGC_FP32_DualNumber* const magnitude, const BGC_FP32_DualQuaternion* const quaternion);
+extern inline void bgc_fp64_dual_quaternion_get_magnitude(BGC_FP64_DualNumber* const magnitude, const BGC_FP64_DualQuaternion* const quaternion);
+
 extern inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* const destination, const BGC_FP32_DualQuaternion* const source);
 extern inline void bgc_fp64_dual_quaternion_copy(BGC_FP64_DualQuaternion* const destination, const BGC_FP64_DualQuaternion* const source);
 

basic-geometry/dual-quaternion.h

@@ -18,6 +18,54 @@ inline void bgc_fp64_dual_quaternion_reset(BGC_FP64_DualQuaternion* const quater
     bgc_fp64_quaternion_reset(&quaternion->dual_part);
 }
 
+// ============== Square Magnitude ============== //
+
+inline void bgc_fp32_dual_quaternion_get_square_magnitude(BGC_FP32_DualNumber* const square_magnitude, const BGC_FP32_DualQuaternion* const quaternion)
+{
+    square_magnitude->real_part = bgc_fp32_quaternion_get_square_magnitude(&quaternion->real_part);
+    square_magnitude->dual_part = 2.0f * bgc_fp32_quaternion_get_dot_product(&quaternion->real_part, &quaternion->dual_part);
+}
+
+inline void bgc_fp64_dual_quaternion_get_square_magnitude(BGC_FP64_DualNumber* const square_magnitude, const BGC_FP64_DualQuaternion* const quaternion)
+{
+    square_magnitude->real_part = bgc_fp64_quaternion_get_square_magnitude(&quaternion->real_part);
+    square_magnitude->dual_part = 2.0 * bgc_fp64_quaternion_get_dot_product(&quaternion->real_part, &quaternion->dual_part);
+}
+
+// ================= Magnitude ================== //
+
+inline void bgc_fp32_dual_quaternion_get_magnitude(BGC_FP32_DualNumber* const magnitude, const BGC_FP32_DualQuaternion* const quaternion)
+{
+    const float square_real_part = bgc_fp32_quaternion_get_square_magnitude(&quaternion->real_part);
+
+    if (square_real_part <= BGC_FP32_SQUARE_EPSILON) {
+        magnitude->real_part = 0.0f;
+        magnitude->dual_part = 0.0f;
+        return;
+    }
+
+    const float real_part = sqrtf(square_real_part);
+
+    magnitude->real_part = real_part;
+    magnitude->dual_part = bgc_fp32_quaternion_get_dot_product(&quaternion->real_part, &quaternion->dual_part) / real_part;
+}
+
+inline void bgc_fp64_dual_quaternion_get_magnitude(BGC_FP64_DualNumber* const magnitude, const BGC_FP64_DualQuaternion* const quaternion)
+{
+    const double square_real_part = bgc_fp64_quaternion_get_square_magnitude(&quaternion->real_part);
+
+    if (square_real_part <= BGC_FP64_SQUARE_EPSILON) {
+        magnitude->real_part = 0.0;
+        magnitude->dual_part = 0.0;
+        return;
+    }
+
+    const double real_part = sqrt(square_real_part);
+
+    magnitude->real_part = real_part;
+    magnitude->dual_part = bgc_fp64_quaternion_get_dot_product(&quaternion->real_part, &quaternion->dual_part) / real_part;
+}
+
 // ==================== Copy ==================== //
 
 inline void bgc_fp32_dual_quaternion_copy(BGC_FP32_DualQuaternion* const destination, const BGC_FP32_DualQuaternion* const source)