Добавлена комбинация трёх версоров одной операцией

basic-geometry/versor.h

@@ -440,6 +440,74 @@ static inline void bg_fp64_versor_combine(const BgFP64Versor* second, const BgFP
     twin->x3 *= multiplier;
 }
 
+// ============ Combination of three ============ //
+
+static inline void bg_fp32_versor_combine3(const BgFP32Versor* third, const BgFP32Versor* second, const BgFP32Versor* first, BgFP32Versor* result)
+{
+    const float s0a = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
+    const float x1a = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
+    const float x2a = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
+    const float x3a = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
+
+    const float s0b = (third->s0 * s0a - third->x1 * x1a) - (third->x2 * x2a + third->x3 * x3a);
+    const float x1b = (third->x1 * s0a + third->s0 * x1a) - (third->x3 * x2a - third->x2 * x3a);
+    const float x2b = (third->x2 * s0a + third->s0 * x2a) - (third->x1 * x3a - third->x3 * x1a);
+    const float x3b = (third->x3 * s0a + third->s0 * x3a) - (third->x2 * x1a - third->x1 * x2a);
+
+    const float square_modulus = (s0b * s0b + x1b * x1b) + (x2b * x2b + x3b * x3b);
+
+    __BgFP32DarkTwinVersor* twin = (__BgFP32DarkTwinVersor*)result;
+
+    twin->s0 = s0b;
+    twin->x1 = x1b;
+    twin->x2 = x2b;
+    twin->x3 = x3b;
+
+    if (1.0f - BG_FP32_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0f + BG_FP32_TWO_EPSYLON) {
+        return;
+    }
+
+    const float multiplier = sqrtf(1.0f / square_modulus);
+
+    twin->s0 *= multiplier;
+    twin->x1 *= multiplier;
+    twin->x2 *= multiplier;
+    twin->x3 *= multiplier;
+}
+
+static inline void bg_fp64_versor_combine3(const BgFP64Versor* third, const BgFP64Versor* second, const BgFP64Versor* first, BgFP64Versor* result)
+{
+    const double s0a = (second->s0 * first->s0 - second->x1 * first->x1) - (second->x2 * first->x2 + second->x3 * first->x3);
+    const double x1a = (second->x1 * first->s0 + second->s0 * first->x1) - (second->x3 * first->x2 - second->x2 * first->x3);
+    const double x2a = (second->x2 * first->s0 + second->s0 * first->x2) - (second->x1 * first->x3 - second->x3 * first->x1);
+    const double x3a = (second->x3 * first->s0 + second->s0 * first->x3) - (second->x2 * first->x1 - second->x1 * first->x2);
+
+    const double s0b = (third->s0 * s0a - third->x1 * x1a) - (third->x2 * x2a + third->x3 * x3a);
+    const double x1b = (third->x1 * s0a + third->s0 * x1a) - (third->x3 * x2a - third->x2 * x3a);
+    const double x2b = (third->x2 * s0a + third->s0 * x2a) - (third->x1 * x3a - third->x3 * x1a);
+    const double x3b = (third->x3 * s0a + third->s0 * x3a) - (third->x2 * x1a - third->x1 * x2a);
+
+    const double square_modulus = (s0b * s0b + x1b * x1b) + (x2b * x2b + x3b * x3b);
+
+    __BgFP64DarkTwinVersor* twin = (__BgFP64DarkTwinVersor*)result;
+
+    twin->s0 = s0b;
+    twin->x1 = x1b;
+    twin->x2 = x2b;
+    twin->x3 = x3b;
+
+    if (1.0 - BG_FP64_TWO_EPSYLON <= square_modulus && square_modulus <= 1.0 + BG_FP64_TWO_EPSYLON) {
+        return;
+    }
+
+    const double multiplier = sqrt(1.0 / square_modulus);
+
+    twin->s0 *= multiplier;
+    twin->x1 *= multiplier;
+    twin->x2 *= multiplier;
+    twin->x3 *= multiplier;
+}
+
 // ================= Exclusion ================== //
 
 static inline void bg_fp32_versor_exclude(const BgFP32Versor* basic, const BgFP32Versor* exclusion, BgFP32Versor* result)