move remaining types

7 files changed, 625 insertions, 610 deletions

diff --git a/source/blender/blenlib/BLI_double2.hh b/source/blender/blenlib/BLI_double2.hh
index 621ac4d01fc..236c429861a 100644
--- a/source/blender/blenlib/BLI_double2.hh
+++ b/source/blender/blenlib/BLI_double2.hh
@@ -22,7 +22,7 @@
 
 #include "BLI_double3.hh"
 
-namespace blender {
+namespace blender::math {
 
 struct double2 {
   double x, y;
@@ -51,78 +51,6 @@ struct double2 {
     return &x;
   }
 
-  double length() const
-  {
-    return len_v2_db(*this);
-  }
-
-  friend double2 operator+(const double2 &a, const double2 &b)
-  {
-    return {a.x + b.x, a.y + b.y};
-  }
-
-  friend double2 operator-(const double2 &a, const double2 &b)
-  {
-    return {a.x - b.x, a.y - b.y};
-  }
-
-  friend double2 operator*(const double2 &a, double b)
-  {
-    return {a.x * b, a.y * b};
-  }
-
-  friend double2 operator/(const double2 &a, double b)
-  {
-    BLI_assert(b != 0.0);
-    return {a.x / b, a.y / b};
-  }
-
-  friend double2 operator*(double a, const double2 &b)
-  {
-    return b * a;
-  }
-
-  friend bool operator==(const double2 &a, const double2 &b)
-  {
-    return a.x == b.x && a.y == b.y;
-  }
-
-  friend bool operator!=(const double2 &a, const double2 &b)
-  {
-    return a.x != b.x || a.y != b.y;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const double2 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ")";
-    return stream;
-  }
-
-  static double dot(const double2 &a, const double2 &b)
-  {
-    return a.x * b.x + a.y * b.y;
-  }
-
-  static double2 interpolate(const double2 &a, const double2 &b, double t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static double2 abs(const double2 &a)
-  {
-    return double2(fabs(a.x), fabs(a.y));
-  }
-
-  static double distance(const double2 &a, const double2 &b)
-  {
-    return (a - b).length();
-  }
-
-  static double distance_squared(const double2 &a, const double2 &b)
-  {
-    return double2::dot(a, b);
-  }
-
   struct isect_result {
     enum {
       LINE_LINE_COLINEAR = -1,
@@ -139,4 +67,81 @@ struct double2 {
                                     const double2 &v4);
 };
 
-}  // namespace blender
+inline double length(const double2 &a)
+{
+  return len_v2_db(a);
+}
+
+inline double2 operator+(const double2 &a, const double2 &b)
+{
+  return {a.x + b.x, a.y + b.y};
+}
+
+inline double2 operator-(const double2 &a, const double2 &b)
+{
+  return {a.x - b.x, a.y - b.y};
+}
+
+inline double2 operator*(const double2 &a, double b)
+{
+  return {a.x * b, a.y * b};
+}
+
+inline double2 operator/(const double2 &a, double b)
+{
+  BLI_assert(b != 0.0);
+  return {a.x / b, a.y / b};
+}
+
+inline double2 operator*(double a, const double2 &b)
+{
+  return b * a;
+}
+
+inline bool operator==(const double2 &a, const double2 &b)
+{
+  return a.x == b.x && a.y == b.y;
+}
+
+inline bool operator!=(const double2 &a, const double2 &b)
+{
+  return a.x != b.x || a.y != b.y;
+}
+
+inline std::ostream &operator<<(std::ostream &stream, const double2 &v)
+{
+  stream << "(" << v.x << ", " << v.y << ")";
+  return stream;
+}
+
+inline double dot(const double2 &a, const double2 &b)
+{
+  return a.x * b.x + a.y * b.y;
+}
+
+inline double2 lerp(const double2 &a, const double2 &b, double t)
+{
+  return a * (1 - t) + b * t;
+}
+
+inline double2 abs(const double2 &a)
+{
+  return double2(fabs(a.x), fabs(a.y));
+}
+
+inline double distance(const double2 &a, const double2 &b)
+{
+  return length(a - b);
+}
+
+inline double distance_squared(const double2 &a, const double2 &b)
+{
+  double2 diff = a - b;
+  return dot(diff, diff);
+}
+
+}  // namespace blender::math
+
+namespace blender {
+using blender::math::double2;
+}
diff --git a/source/blender/blenlib/BLI_double3.hh b/source/blender/blenlib/BLI_double3.hh
index 5b6204935d7..0d60148e1de 100644
--- a/source/blender/blenlib/BLI_double3.hh
+++ b/source/blender/blenlib/BLI_double3.hh
@@ -25,7 +25,7 @@
 #include "BLI_math_vector.h"
 #include "BLI_span.hh"
 
-namespace blender {
+namespace blender::math {
 
 struct double3 {
   double x, y, z;
@@ -62,184 +62,188 @@ struct double3 {
     return &x;
   }
 
-  double normalize_and_get_length()
-  {
-    return normalize_v3_db(*this);
-  }
-
-  double3 normalized() const
-  {
-    double3 result;
-    normalize_v3_v3_db(result, *this);
-    return result;
-  }
-
-  double length() const
-  {
-    return len_v3_db(*this);
-  }
-
-  double length_squared() const
-  {
-    return len_squared_v3_db(*this);
-  }
-
-  void reflect(const double3 &normal)
-  {
-    *this = this->reflected(normal);
-  }
-
-  double3 reflected(const double3 &normal) const
-  {
-    double3 result;
-    reflect_v3_v3v3_db(result, *this, normal);
-    return result;
-  }
-
-  static double3 safe_divide(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    result.x = (b.x == 0.0) ? 0.0 : a.x / b.x;
-    result.y = (b.y == 0.0) ? 0.0 : a.y / b.y;
-    result.z = (b.z == 0.0) ? 0.0 : a.z / b.z;
-    return result;
-  }
-
-  void invert()
-  {
-    x = -x;
-    y = -y;
-    z = -z;
-  }
-
-  friend double3 operator+(const double3 &a, const double3 &b)
-  {
-    return {a.x + b.x, a.y + b.y, a.z + b.z};
-  }
-
-  void operator+=(const double3 &b)
-  {
-    this->x += b.x;
-    this->y += b.y;
-    this->z += b.z;
-  }
-
-  friend double3 operator-(const double3 &a, const double3 &b)
-  {
-    return {a.x - b.x, a.y - b.y, a.z - b.z};
-  }
-
-  friend double3 operator-(const double3 &a)
-  {
-    return {-a.x, -a.y, -a.z};
-  }
-
-  void operator-=(const double3 &b)
-  {
-    this->x -= b.x;
-    this->y -= b.y;
-    this->z -= b.z;
-  }
-
-  void operator*=(const double &scalar)
-  {
-    this->x *= scalar;
-    this->y *= scalar;
-    this->z *= scalar;
-  }
-
-  void operator*=(const double3 &other)
-  {
-    this->x *= other.x;
-    this->y *= other.y;
-    this->z *= other.z;
-  }
-
-  friend double3 operator*(const double3 &a, const double3 &b)
-  {
-    return {a.x * b.x, a.y * b.y, a.z * b.z};
-  }
-
-  friend double3 operator*(const double3 &a, const double &b)
-  {
-    return {a.x * b, a.y * b, a.z * b};
-  }
-
-  friend double3 operator*(const double &a, const double3 &b)
-  {
-    return b * a;
-  }
-
-  friend double3 operator/(const double3 &a, const double &b)
-  {
-    BLI_assert(b != 0.0);
-    return {a.x / b, a.y / b, a.z / b};
-  }
-
-  friend bool operator==(const double3 &a, const double3 &b)
-  {
-    return a.x == b.x && a.y == b.y && a.z == b.z;
-  }
-
-  friend bool operator!=(const double3 &a, const double3 &b)
-  {
-    return a.x != b.x || a.y != b.y || a.z != b.z;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const double3 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
-    return stream;
-  }
-
-  static double dot(const double3 &a, const double3 &b)
-  {
-    return a.x * b.x + a.y * b.y + a.z * b.z;
-  }
-
-  static double3 cross_high_precision(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    cross_v3_v3v3_db(result, a, b);
-    return result;
-  }
-
-  static double3 project(const double3 &a, const double3 &b)
-  {
-    double3 result;
-    project_v3_v3v3_db(result, a, b);
-    return result;
-  }
-
-  static double distance(const double3 &a, const double3 &b)
-  {
-    return (a - b).length();
-  }
-
-  static double distance_squared(const double3 &a, const double3 &b)
-  {
-    return double3::dot(a, b);
-  }
-
-  static double3 interpolate(const double3 &a, const double3 &b, double t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static double3 abs(const double3 &a)
-  {
-    return double3(fabs(a.x), fabs(a.y), fabs(a.z));
-  }
-
-  static int dominant_axis(const double3 &a)
-  {
-    double x = (a.x >= 0) ? a.x : -a.x;
-    double y = (a.y >= 0) ? a.y : -a.y;
-    double z = (a.z >= 0) ? a.z : -a.z;
-    return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
-  }
-
   static double3 cross_poly(Span<double3> poly);
 };
 
-}  // namespace blender
+inline double normalize_and_get_length(double3 &a)
+{
+  return normalize_v3_db(a);
+}
+
+inline double3 normalized(const double3 &a)
+{
+  double3 result;
+  normalize_v3_v3_db(result, a);
+  return result;
+}
+
+inline double length(const double3 &a)
+{
+  return len_v3_db(a);
+}
+
+inline double length_squared(const double3 &a)
+{
+  return len_squared_v3_db(a);
+}
+
+inline double3 reflected(const double3 &a, const double3 &normal)
+{
+  double3 result;
+  reflect_v3_v3v3_db(result, a, normal);
+  return result;
+}
+
+inline void reflect(double3 &a, const double3 &normal)
+{
+  a = reflected(a, normal);
+}
+
+inline double3 safe_divide(const double3 &a, const double3 &b)
+{
+  double3 result;
+  result.x = (b.x == 0.0) ? 0.0 : a.x / b.x;
+  result.y = (b.y == 0.0) ? 0.0 : a.y / b.y;
+  result.z = (b.z == 0.0) ? 0.0 : a.z / b.z;
+  return result;
+}
+
+inline void negate(double3 &a)
+{
+  a.x = -a.x;
+  a.y = -a.y;
+  a.z = -a.z;
+}
+
+inline double3 operator+(const double3 &a, const double3 &b)
+{
+  return {a.x + b.x, a.y + b.y, a.z + b.z};
+}
+
+inline void operator+=(double3 &a, const double3 &b)
+{
+  a.x += b.x;
+  a.y += b.y;
+  a.z += b.z;
+}
+
+inline double3 operator-(const double3 &a, const double3 &b)
+{
+  return {a.x - b.x, a.y - b.y, a.z - b.z};
+}
+
+inline double3 operator-(const double3 &a)
+{
+  return {-a.x, -a.y, -a.z};
+}
+
+inline void operator-=(double3 &a, const double3 &b)
+{
+  a.x -= b.x;
+  a.y -= b.y;
+  a.z -= b.z;
+}
+
+inline void operator*=(double3 &a, const double &scalar)
+{
+  a.x *= scalar;
+  a.y *= scalar;
+  a.z *= scalar;
+}
+
+inline void operator*=(double3 &a, const double3 &other)
+{
+  a.x *= other.x;
+  a.y *= other.y;
+  a.z *= other.z;
+}
+
+inline double3 operator*(const double3 &a, const double3 &b)
+{
+  return {a.x * b.x, a.y * b.y, a.z * b.z};
+}
+
+inline double3 operator*(const double3 &a, const double &b)
+{
+  return {a.x * b, a.y * b, a.z * b};
+}
+
+inline double3 operator*(const double &a, const double3 &b)
+{
+  return b * a;
+}
+
+inline double3 operator/(const double3 &a, const double &b)
+{
+  BLI_assert(b != 0.0);
+  return {a.x / b, a.y / b, a.z / b};
+}
+
+inline bool operator==(const double3 &a, const double3 &b)
+{
+  return a.x == b.x && a.y == b.y && a.z == b.z;
+}
+
+inline bool operator!=(const double3 &a, const double3 &b)
+{
+  return a.x != b.x || a.y != b.y || a.z != b.z;
+}
+
+inline std::ostream &operator<<(std::ostream &stream, const double3 &v)
+{
+  stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
+  return stream;
+}
+
+inline double dot(const double3 &a, const double3 &b)
+{
+  return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+inline double3 cross_high_precision(const double3 &a, const double3 &b)
+{
+  double3 result;
+  cross_v3_v3v3_db(result, a, b);
+  return result;
+}
+
+inline double3 project(const double3 &a, const double3 &b)
+{
+  double3 result;
+  project_v3_v3v3_db(result, a, b);
+  return result;
+}
+
+inline double distance(const double3 &a, const double3 &b)
+{
+  return length(a - b);
+}
+
+inline double distance_squared(const double3 &a, const double3 &b)
+{
+  return dot(a, b);
+}
+
+inline double3 lerp(const double3 &a, const double3 &b, double t)
+{
+  return a * (1 - t) + b * t;
+}
+
+inline double3 abs(const double3 &a)
+{
+  return double3(fabs(a.x), fabs(a.y), fabs(a.z));
+}
+
+inline int dominant_axis(const double3 &a)
+{
+  double x = (a.x >= 0) ? a.x : -a.x;
+  double y = (a.y >= 0) ? a.y : -a.y;
+  double z = (a.z >= 0) ? a.z : -a.z;
+  return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
+}
+
+}  // namespace blender::math
+
+namespace blender {
+using math::double3;
+}
diff --git a/source/blender/blenlib/BLI_mpq2.hh b/source/blender/blenlib/BLI_mpq2.hh
index 40e227019ce..de88bd82890 100644
--- a/source/blender/blenlib/BLI_mpq2.hh
+++ b/source/blender/blenlib/BLI_mpq2.hh
@@ -25,7 +25,7 @@
 #  include "BLI_math_mpq.hh"
 #  include "BLI_mpq3.hh"
 
-namespace blender {
+namespace blender::math {
 
 struct mpq2 {
   mpq_class x, y;
@@ -80,85 +80,6 @@ struct mpq2 {
     return &x;
   }
 
-  /**
-   * Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of doubles.
-   */
-  mpq_class length() const
-  {
-    mpq_class lsquared = dot(*this, *this);
-    return mpq_class(sqrt(lsquared.get_d()));
-  }
-
-  friend mpq2 operator+(const mpq2 &a, const mpq2 &b)
-  {
-    return {a.x + b.x, a.y + b.y};
-  }
-
-  friend mpq2 operator-(const mpq2 &a, const mpq2 &b)
-  {
-    return {a.x - b.x, a.y - b.y};
-  }
-
-  friend mpq2 operator*(const mpq2 &a, mpq_class b)
-  {
-    return {a.x * b, a.y * b};
-  }
-
-  friend mpq2 operator/(const mpq2 &a, mpq_class b)
-  {
-    BLI_assert(b != 0);
-    return {a.x / b, a.y / b};
-  }
-
-  friend mpq2 operator*(mpq_class a, const mpq2 &b)
-  {
-    return b * a;
-  }
-
-  friend bool operator==(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x == b.x && a.y == b.y;
-  }
-
-  friend bool operator!=(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x != b.x || a.y != b.y;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const mpq2 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ")";
-    return stream;
-  }
-
-  static mpq_class dot(const mpq2 &a, const mpq2 &b)
-  {
-    return a.x * b.x + a.y * b.y;
-  }
-
-  static mpq2 interpolate(const mpq2 &a, const mpq2 &b, mpq_class t)
-  {
-    return a * (1 - t) + b * t;
-  }
-
-  static mpq2 abs(const mpq2 &a)
-  {
-    mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
-    return mpq2(abs_x, abs_y);
-  }
-
-  static mpq_class distance(const mpq2 &a, const mpq2 &b)
-  {
-    return (a - b).length();
-  }
-
-  static mpq_class distance_squared(const mpq2 &a, const mpq2 &b)
-  {
-    return dot(a, b);
-  }
-
   struct isect_result {
     enum {
       LINE_LINE_COLINEAR = -1,
@@ -178,6 +99,89 @@ struct mpq2 {
   uint64_t hash() const;
 };
 
-}  // namespace blender
+inline mpq2 operator+(const mpq2 &a, const mpq2 &b)
+{
+  return {a.x + b.x, a.y + b.y};
+}
+
+inline mpq2 operator-(const mpq2 &a, const mpq2 &b)
+{
+  return {a.x - b.x, a.y - b.y};
+}
+
+inline mpq2 operator*(const mpq2 &a, mpq_class b)
+{
+  return {a.x * b, a.y * b};
+}
+
+inline mpq2 operator/(const mpq2 &a, mpq_class b)
+{
+  BLI_assert(b != 0);
+  return {a.x / b, a.y / b};
+}
+
+inline mpq2 operator*(mpq_class a, const mpq2 &b)
+{
+  return b * a;
+}
+
+inline bool operator==(const mpq2 &a, const mpq2 &b)
+{
+  return a.x == b.x && a.y == b.y;
+}
+
+inline bool operator!=(const mpq2 &a, const mpq2 &b)
+{
+  return a.x != b.x || a.y != b.y;
+}
+
+inline std::ostream &operator<<(std::ostream &stream, const mpq2 &v)
+{
+  stream << "(" << v.x << ", " << v.y << ")";
+  return stream;
+}
+
+inline mpq_class dot(const mpq2 &a, const mpq2 &b)
+{
+  return a.x * b.x + a.y * b.y;
+}
+
+/**
+ * Cannot do this exactly in rational arithmetic!
+ * Approximate by going in and out of doubles.
+ */
+inline mpq_class length(const mpq2 &a)
+{
+  mpq_class lsquared = dot(a, a);
+  return mpq_class(sqrt(lsquared.get_d()));
+}
+
+inline mpq2 lerp(const mpq2 &a, const mpq2 &b, mpq_class t)
+{
+  return a * (1 - t) + b * t;
+}
+
+inline mpq2 abs(const mpq2 &a)
+{
+  mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
+  mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
+  return mpq2(abs_x, abs_y);
+}
+
+inline mpq_class distance(const mpq2 &a, const mpq2 &b)
+{
+  return length(a - b);
+}
+
+inline mpq_class distance_squared(const mpq2 &a, const mpq2 &b)
+{
+  return dot(a, b);
+}
+
+}  // namespace blender::math
+
+namespace blender {
+using math::mpq2;
+}
 
 #endif /* WITH_GMP */
diff --git a/source/blender/blenlib/BLI_mpq3.hh b/source/blender/blenlib/BLI_mpq3.hh
index fb5e2b61cdb..66200eea352 100644
--- a/source/blender/blenlib/BLI_mpq3.hh
+++ b/source/blender/blenlib/BLI_mpq3.hh
@@ -28,7 +28,7 @@
 #  include "BLI_math_mpq.hh"
 #  include "BLI_span.hh"
 
-namespace blender {
+namespace blender::math {
 
 struct mpq3 {
   mpq_class x, y, z;
@@ -65,217 +65,220 @@ struct mpq3 {
     return &x;
   }
 
-  /* Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of doubles.
-   */
-  mpq_class normalize_and_get_length()
-  {
-    double dv[3] = {x.get_d(), y.get_d(), z.get_d()};
-    double len = normalize_v3_db(dv);
-    this->x = mpq_class(dv[0]);
-    this->y = mpq_class(dv[1]);
-    this->z = mpq_class(dv[2]);
-    return len;
-  }
-
-  mpq3 normalized() const
-  {
-    double dv[3] = {x.get_d(), y.get_d(), z.get_d()};
-    double dr[3];
-    normalize_v3_v3_db(dr, dv);
-    return mpq3(mpq_class(dr[0]), mpq_class(dr[1]), mpq_class(dr[2]));
-  }
-
-  /* Cannot do this exactly in rational arithmetic!
-   * Approximate by going in and out of double.
-   */
-  mpq_class length() const
-  {
-    mpq_class lsquared = this->length_squared();
-    double dsquared = lsquared.get_d();
-    double d = sqrt(dsquared);
-    return mpq_class(d);
-  }
-
-  mpq_class length_squared() const
-  {
-    return x * x + y * y + z * z;
-  }
-
-  void reflect(const mpq3 &normal)
-  {
-    *this = this->reflected(normal);
-  }
-
-  mpq3 reflected(const mpq3 &normal) const
-  {
-    mpq3 result;
-    const mpq_class dot2 = 2 * dot(*this, normal);
-    result.x = this->x - (dot2 * normal.x);
-    result.y = this->y - (dot2 * normal.y);
-    result.z = this->z - (dot2 * normal.z);
-    return result;
-  }
-
-  static mpq3 safe_divide(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 result;
-    result.x = (b.x == 0) ? mpq_class(0) : a.x / b.x;
-    result.y = (b.y == 0) ? mpq_class(0) : a.y / b.y;
-    result.z = (b.z == 0) ? mpq_class(0) : a.z / b.z;
-    return result;
-  }
-
-  void invert()
-  {
-    x = -x;
-    y = -y;
-    z = -z;
-  }
-
-  friend mpq3 operator+(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a.x + b.x, a.y + b.y, a.z + b.z);
-  }
-
-  void operator+=(const mpq3 &b)
-  {
-    this->x += b.x;
-    this->y += b.y;
-    this->z += b.z;
-  }
-
-  friend mpq3 operator-(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a.x - b.x, a.y - b.y, a.z - b.z);
-  }
-
-  friend mpq3 operator-(const mpq3 &a)
-  {
-    return mpq3(-a.x, -a.y, -a.z);
-  }
-
-  void operator-=(const mpq3 &b)
-  {
-    this->x -= b.x;
-    this->y -= b.y;
-    this->z -= b.z;
-  }
-
-  void operator*=(mpq_class scalar)
-  {
-    this->x *= scalar;
-    this->y *= scalar;
-    this->z *= scalar;
-  }
-
-  void operator*=(const mpq3 &other)
-  {
-    this->x *= other.x;
-    this->y *= other.y;
-    this->z *= other.z;
-  }
-
-  friend mpq3 operator*(const mpq3 &a, const mpq3 &b)
-  {
-    return {a.x * b.x, a.y * b.y, a.z * b.z};
-  }
-
-  friend mpq3 operator*(const mpq3 &a, const mpq_class &b)
-  {
-    return mpq3(a.x * b, a.y * b, a.z * b);
-  }
-
-  friend mpq3 operator*(const mpq_class &a, const mpq3 &b)
-  {
-    return mpq3(a * b.x, a * b.y, a * b.z);
-  }
-
-  friend mpq3 operator/(const mpq3 &a, const mpq_class &b)
-  {
-    BLI_assert(b != 0);
-    return mpq3(a.x / b, a.y / b, a.z / b);
-  }
-
-  friend bool operator==(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x == b.x && a.y == b.y && a.z == b.z;
-  }
-
-  friend bool operator!=(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x != b.x || a.y != b.y || a.z != b.z;
-  }
-
-  friend std::ostream &operator<<(std::ostream &stream, const mpq3 &v)
-  {
-    stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
-    return stream;
-  }
-
-  static mpq_class dot(const mpq3 &a, const mpq3 &b)
-  {
-    return a.x * b.x + a.y * b.y + a.z * b.z;
-  }
-
-  static mpq3 cross(const mpq3 &a, const mpq3 &b)
-  {
-    return mpq3(a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]);
-  }
-
-  static mpq3 cross_high_precision(const mpq3 &a, const mpq3 &b)
-  {
-    return cross(a, b);
-  }
-
-  static mpq3 project(const mpq3 &a, const mpq3 &b)
-  {
-    const mpq_class mul = mpq3::dot(a, b) / mpq3::dot(b, b);
-    return mpq3(mul * b[0], mul * b[1], mul * b[2]);
-  }
-
-  static mpq_class distance(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 diff(a.x - b.x, a.y - b.y, a.z - b.z);
-    return diff.length();
-  }
-
-  static mpq_class distance_squared(const mpq3 &a, const mpq3 &b)
-  {
-    mpq3 diff(a.x - b.x, a.y - b.y, a.z - b.z);
-    return mpq3::dot(diff, diff);
-  }
-
-  static mpq3 interpolate(const mpq3 &a, const mpq3 &b, mpq_class t)
-  {
-    mpq_class s = 1 - t;
-    return mpq3(a.x * s + b.x * t, a.y * s + b.y * t, a.z * s + b.z * t);
-  }
-
-  static mpq3 abs(const mpq3 &a)
-  {
-    mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
-    mpq_class abs_z = (a.z >= 0) ? a.z : -a.z;
-    return mpq3(abs_x, abs_y, abs_z);
-  }
-
-  static int dominant_axis(const mpq3 &a)
-  {
-    mpq_class x = (a.x >= 0) ? a.x : -a.x;
-    mpq_class y = (a.y >= 0) ? a.y : -a.y;
-    mpq_class z = (a.z >= 0) ? a.z : -a.z;
-    return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
-  }
-
   static mpq3 cross_poly(Span<mpq3> poly);
 
   /** There is a sensible use for hashing on exact arithmetic types. */
   uint64_t hash() const;
 };
 
-uint64_t hash_mpq_class(const mpq_class &value);
+/* Cannot do this exactly in rational arithmetic!
+ * Approximate by going in and out of doubles.
+ */
+inline mpq_class normalize_and_get_length(mpq3 &a)
+{
+  double dv[3] = {a.x.get_d(), a.y.get_d(), a.z.get_d()};
+  double len = normalize_v3_db(dv);
+  a.x = mpq_class(dv[0]);
+  a.y = mpq_class(dv[1]);
+  a.z = mpq_class(dv[2]);
+  return len;
+}
+
+inline mpq3 normalized(const mpq3 &a)
+{
+  double dv[3] = {a.x.get_d(), a.y.get_d(), a.z.get_d()};
+  double dr[3];
+  normalize_v3_v3_db(dr, dv);
+  return mpq3(mpq_class(dr[0]), mpq_class(dr[1]), mpq_class(dr[2]));
+}
+
+inline mpq_class length_squared(const mpq3 &a)
+{
+  return a.x * a.x + a.y * a.y + a.z * a.z;
+}
+
+/* Cannot do this exactly in rational arithmetic!
+ * Approximate by going in and out of double.
+ */
+inline mpq_class length(const mpq3 &a)
+{
+  mpq_class lsquared = length_squared(a);
+  double dsquared = lsquared.get_d();
+  double d = sqrt(dsquared);
+  return mpq_class(d);
+}
+
+inline mpq_class dot(const mpq3 &a, const mpq3 &b)
+{
+  return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+inline mpq3 reflected(const mpq3 &a, const mpq3 &normal)
+{
+  mpq3 result;
+  const mpq_class dot2 = 2 * dot(a, normal);
+  result.x = a.x - (dot2 * normal.x);
+  result.y = a.y - (dot2 * normal.y);
+  result.z = a.z - (dot2 * normal.z);
+  return result;
+}
+
+inline void reflect(mpq3 &a, const mpq3 &normal)
+{
+  a = reflected(a, normal);
+}
+
+inline mpq3 safe_divide(const mpq3 &a, const mpq3 &b)
+{
+  mpq3 result;
+  result.x = (b.x == 0) ? mpq_class(0) : a.x / b.x;
+  result.y = (b.y == 0) ? mpq_class(0) : a.y / b.y;
+  result.z = (b.z == 0) ? mpq_class(0) : a.z / b.z;
+  return result;
+}
+
+inline void negate(mpq3 &a)
+{
+  a.x = -a.x;
+  a.y = -a.y;
+  a.z = -a.z;
+}
+
+inline mpq3 operator+(const mpq3 &a, const mpq3 &b)
+{
+  return mpq3(a.x + b.x, a.y + b.y, a.z + b.z);
+}
+
+inline void operator+=(mpq3 &a, const mpq3 &b)
+{
+  a.x += b.x;
+  a.y += b.y;
+  a.z += b.z;
+}
+
+inline mpq3 operator-(const mpq3 &a, const mpq3 &b)
+{
+  return mpq3(a.x - b.x, a.y - b.y, a.z - b.z);
+}
+
+inline mpq3 operator-(const mpq3 &a)
+{
+  return mpq3(-a.x, -a.y, -a.z);
+}
+
+inline void operator-=(mpq3 &a, const mpq3 &b)
+{
+  a.x -= b.x;
+  a.y -= b.y;
+  a.z -= b.z;
+}
+
+inline void operator*=(mpq3 &a, mpq_class scalar)
+{
+  a.x *= scalar;
+  a.y *= scalar;
+  a.z *= scalar;
+}
+
+inline void operator*=(mpq3 &a, const mpq3 &other)
+{
+  a.x *= other.x;
+  a.y *= other.y;
+  a.z *= other.z;
+}
+
+inline mpq3 operator*(const mpq3 &a, const mpq3 &b)
+{
+  return {a.x * b.x, a.y * b.y, a.z * b.z};
+}
+
+inline mpq3 operator*(const mpq3 &a, const mpq_class &b)
+{
+  return mpq3(a.x * b, a.y * b, a.z * b);
+}
+
+inline mpq3 operator*(const mpq_class &a, const mpq3 &b)
+{
+  return mpq3(a * b.x, a * b.y, a * b.z);
+}
+
+inline mpq3 operator/(const mpq3 &a, const mpq_class &b)
+{
+  BLI_assert(b != 0);
+  return mpq3(a.x / b, a.y / b, a.z / b);
+}
+
+inline bool operator==(const mpq3 &a, const mpq3 &b)
+{
+  return a.x == b.x && a.y == b.y && a.z == b.z;
+}
+
+inline bool operator!=(const mpq3 &a, const mpq3 &b)
+{
+  return a.x != b.x || a.y != b.y || a.z != b.z;
+}
+
+inline std::ostream &operator<<(std::ostream &stream, const mpq3 &v)
+{
+  stream << "(" << v.x << ", " << v.y << ", " << v.z << ")";
+  return stream;
+}
+
+inline mpq3 cross(const mpq3 &a, const mpq3 &b)
+{
+  return mpq3(a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]);
+}
+
+inline mpq3 cross_high_precision(const mpq3 &a, const mpq3 &b)
+{
+  return cross(a, b);
+}
+
+inline mpq3 project(const mpq3 &a, const mpq3 &b)
+{
+  const mpq_class mul = dot(a, b) / dot(b, b);
+  return mpq3(mul * b[0], mul * b[1], mul * b[2]);
+}
+
+inline mpq_class distance(const mpq3 &a, const mpq3 &b)
+{
+  return length(a - b);
+}
+
+inline mpq_class distance_squared(const mpq3 &a, const mpq3 &b)
+{
+  mpq3 diff(a.x - b.x, a.y - b.y, a.z - b.z);
+  return dot(diff, diff);
+}
+
+inline mpq3 lerp(const mpq3 &a, const mpq3 &b, mpq_class t)
+{
+  mpq_class s = 1 - t;
+  return mpq3(a.x * s + b.x * t, a.y * s + b.y * t, a.z * s + b.z * t);
+}
+
+inline mpq3 abs(const mpq3 &a)
+{
+  mpq_class abs_x = (a.x >= 0) ? a.x : -a.x;
+  mpq_class abs_y = (a.y >= 0) ? a.y : -a.y;
+  mpq_class abs_z = (a.z >= 0) ? a.z : -a.z;
+  return mpq3(abs_x, abs_y, abs_z);
+}
+
+inline int dominant_axis(const mpq3 &a)
+{
+  mpq_class x = (a.x >= 0) ? a.x : -a.x;
+  mpq_class y = (a.y >= 0) ? a.y : -a.y;
+  mpq_class z = (a.z >= 0) ? a.z : -a.z;
+  return ((x > y) ? ((x > z) ? 0 : 2) : ((y > z) ? 1 : 2));
+}
+
+}  // namespace blender::math
 
+namespace blender {
+using math::mpq3;
+
+uint64_t hash_mpq_class(const mpq_class &value);
 }  // namespace blender
 
 #endif /* WITH_GMP */
diff --git a/source/blender/blenlib/intern/delaunay_2d.cc b/source/blender/blenlib/intern/delaunay_2d.cc
index f0b65a55816..a7693fea136 100644
--- a/source/blender/blenlib/intern/delaunay_2d.cc
+++ b/source/blender/blenlib/intern/delaunay_2d.cc
@@ -730,11 +730,11 @@ bool in_line<mpq_class>(const FatCo<mpq_class> &a,
   }
   vec2<mpq_class> exact_ab = b.exact - a.exact;
   vec2<mpq_class> exact_ac = c.exact - a.exact;
-  if (vec2<mpq_class>::dot(exact_ab, exact_ac) < 0) {
+  if (dot(exact_ab, exact_ac) < 0) {
     return false;
   }
   vec2<mpq_class> exact_bc = c.exact - b.exact;
-  return vec2<mpq_class>::dot(exact_bc, exact_ac) >= 0;
+  return dot(exact_bc, exact_ac) >= 0;
 }
 #endif
 
@@ -743,11 +743,11 @@ bool in_line<double>(const FatCo<double> &a, const FatCo<double> &b, const FatCo
 {
   vec2<double> ab = b.approx - a.approx;
   vec2<double> ac = c.approx - a.approx;
-  if (vec2<double>::dot(ab, ac) < 0) {
+  if (dot(ab, ac) < 0) {
     return false;
   }
   vec2<double> bc = c.approx - b.approx;
-  return vec2<double>::dot(bc, ac) >= 0;
+  return dot(bc, ac) >= 0;
 }
 
 template<> CDTVert<double>::CDTVert(const vec2<double> &pt)
@@ -1041,7 +1041,7 @@ template<typename T> CDTEdge<T> *CDTArrangement<T>::split_edge(SymEdge<T> *se, T
   SymEdge<T> *sesymprev = prev(sesym);
   SymEdge<T> *sesymprevsym = sym(sesymprev);
   SymEdge<T> *senext = se->next;
-  CDTVert<T> *v = this->add_vert(vec2<T>::interpolate(*a, *b, lambda));
+  CDTVert<T> *v = this->add_vert(lerp(*a, *b, lambda));
   CDTEdge<T> *e = this->add_edge(v, se->next->vert, se->face, sesym->face);
   sesym->vert = v;
   SymEdge<T> *newse = &e->symedges[0];
@@ -1673,7 +1673,7 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
 #else
       if (true) {
 #endif
-        double len_ab = vec2<double>::distance(va->co.approx, vb->co.approx);
+        double len_ab = distance(va->co.approx, vb->co.approx);
         if (lambda * len_ab <= epsilon) {
           fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
         }
@@ -1727,8 +1727,8 @@ void fill_crossdata_for_intersect(const FatCo<T> &curco,
       break;
     }
     case vec2<T>::isect_result::LINE_LINE_COLINEAR: {
-      if (vec2<double>::distance_squared(va->co.approx, v2->co.approx) <=
-          vec2<double>::distance_squared(vb->co.approx, v2->co.approx)) {
+      if (distance_squared(va->co.approx, v2->co.approx) <=
+          distance_squared(vb->co.approx, v2->co.approx)) {
         fill_crossdata_for_through_vert(va, se_vcva, cd, cd_next);
       }
       else {
@@ -1805,7 +1805,7 @@ void get_next_crossing_from_edge(CrossData<T> *cd,
 {
   CDTVert<T> *va = cd->in->vert;
   CDTVert<T> *vb = cd->in->next->vert;
-  vec2<T> curco = vec2<T>::interpolate(va->co.exact, vb->co.exact, cd->lambda);
+  vec2<T> curco = lerp(va->co.exact, vb->co.exact, cd->lambda);
   FatCo<T> fat_curco(curco);
   SymEdge<T> *se_ac = sym(cd->in)->next;
   CDTVert<T> *vc = se_ac->next->vert;
@@ -2332,7 +2332,7 @@ template<typename T> void remove_non_constraint_edges_leave_valid_bmesh(CDT_stat
       dissolvable_edges[i].e = e;
       const vec2<double> &co1 = e->symedges[0].vert->co.approx;
       const vec2<double> &co2 = e->symedges[1].vert->co.approx;
-      dissolvable_edges[i].len_squared = vec2<double>::distance_squared(co1, co2);
+      dissolvable_edges[i].len_squared = distance_squared(co1, co2);
       i++;
     }
   }
diff --git a/source/blender/blenlib/intern/mesh_boolean.cc b/source/blender/blenlib/intern/mesh_boolean.cc
index 88d90a7816f..8335a6b951e 100644
--- a/source/blender/blenlib/intern/mesh_boolean.cc
+++ b/source/blender/blenlib/intern/mesh_boolean.cc
@@ -1561,13 +1561,13 @@ static Edge find_good_sorting_edge(const Vert *testp,
   ordinate[axis_next] = -abscissa[axis];
   ordinate[axis_next_next] = 0;
   /* By construction, dot(abscissa, ordinate) == 0, so they are perpendicular. */
-  mpq3 normal = mpq3::cross(abscissa, ordinate);
+  mpq3 normal = cross(abscissa, ordinate);
   if (dbg_level > 0) {
     std::cout << "abscissa = " << abscissa << "\n";
     std::cout << "ordinate = " << ordinate << "\n";
     std::cout << "normal = " << normal << "\n";
   }
-  mpq_class nlen2 = normal.length_squared();
+  mpq_class nlen2 = length_squared(normal);
   mpq_class max_abs_slope = -1;
   Edge esort;
   const Vector<Edge> &edges = tmtopo.vert_edges(closestp);
@@ -1576,12 +1576,12 @@ static Edge find_good_sorting_edge(const Vert *testp,
     const mpq3 &co_other = v_other->co_exact;
     mpq3 evec = co_other - co_closest;
     /* Get projection of evec onto plane of abscissa and ordinate. */
-    mpq3 proj_evec = evec - (mpq3::dot(evec, normal) / nlen2) * normal;
+    mpq3 proj_evec = evec - (dot(evec, normal) / nlen2) * normal;
     /* The projection calculations along the abscissa and ordinate should
      * be scaled by 1/abscissa and 1/ordinate respectively,
      * but we can skip: it won't affect which `evec` has the maximum slope. */
-    mpq_class evec_a = mpq3::dot(proj_evec, abscissa);
-    mpq_class evec_o = mpq3::dot(proj_evec, ordinate);
+    mpq_class evec_a = dot(proj_evec, abscissa);
+    mpq_class evec_o = dot(proj_evec, ordinate);
     if (dbg_level > 0) {
       std::cout << "e = " << e << "\n";
       std::cout << "v_other = " << v_other << "\n";
@@ -1700,8 +1700,8 @@ static mpq_class closest_on_tri_to_point(
   mpq3 ab = b - a;
   mpq3 ac = c - a;
   mpq3 ap = p - a;
-  mpq_class d1 = mpq3::dot(ab, ap);
-  mpq_class d2 = mpq3::dot(ac, ap);
+  mpq_class d1 = dot(ab, ap);
+  mpq_class d2 = dot(ac, ap);
   if (d1 <= 0 && d2 <= 0) {
     /* Barycentric coordinates (1,0,0). */
     *r_edge = -1;
@@ -1709,12 +1709,12 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = a\n";
     }
-    return mpq3::distance_squared(p, a);
+    return distance_squared(p, a);
   }
   /* Check if p in vertex region outside b. */
   mpq3 bp = p - b;
-  mpq_class d3 = mpq3::dot(ab, bp);
-  mpq_class d4 = mpq3::dot(ac, bp);
+  mpq_class d3 = dot(ab, bp);
+  mpq_class d4 = dot(ac, bp);
   if (d3 >= 0 && d4 <= d3) {
     /* Barycentric coordinates (0,1,0). */
     *r_edge = -1;
@@ -1722,7 +1722,7 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = b\n";
     }
-    return mpq3::distance_squared(p, b);
+    return distance_squared(p, b);
   }
   /* Check if p in region of ab. */
   mpq_class vc = d1 * d4 - d3 * d2;
@@ -1735,12 +1735,12 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = on ab at " << r << "\n";
     }
-    return mpq3::distance_squared(p, r);
+    return distance_squared(p, r);
   }
   /* Check if p in vertex region outside c. */
   mpq3 cp = p - c;
-  mpq_class d5 = mpq3::dot(ab, cp);
-  mpq_class d6 = mpq3::dot(ac, cp);
+  mpq_class d5 = dot(ab, cp);
+  mpq_class d6 = dot(ac, cp);
   if (d6 >= 0 && d5 <= d6) {
     /* Barycentric coordinates (0,0,1). */
     *r_edge = -1;
@@ -1748,7 +1748,7 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = c\n";
     }
-    return mpq3::distance_squared(p, c);
+    return distance_squared(p, c);
   }
   /* Check if p in edge region of ac. */
   mpq_class vb = d5 * d2 - d1 * d6;
@@ -1761,7 +1761,7 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = on ac at " << r << "\n";
     }
-    return mpq3::distance_squared(p, r);
+    return distance_squared(p, r);
   }
   /* Check if p in edge region of bc. */
   mpq_class va = d3 * d6 - d5 * d4;
@@ -1776,7 +1776,7 @@ static mpq_class closest_on_tri_to_point(
     if (dbg_level > 0) {
       std::cout << "  answer = on bc at " << r << "\n";
     }
-    return mpq3::distance_squared(p, r);
+    return distance_squared(p, r);
   }
   /* p inside face region. Compute barycentric coordinates (u,v,w). */
   mpq_class denom = 1 / (va + vb + vc);
@@ -1790,7 +1790,7 @@ static mpq_class closest_on_tri_to_point(
   if (dbg_level > 0) {
     std::cout << "  answer = inside at " << r << "\n";
   }
-  return mpq3::distance_squared(p, r);
+  return distance_squared(p, r);
 }
 
 struct ComponentContainer {
@@ -2375,13 +2375,12 @@ static double generalized_winding_number(const IMesh &tm,
       /* Calculate the solid angle of abc relative to origin.
        * See "The Solid Angle of a Plane Triangle" by Oosterom and Strackee
        * for the derivation of the formula. */
-      double alen = a.length();
-      double blen = b.length();
-      double clen = c.length();
-      double3 bxc = double3::cross_high_precision(b, c);
-      double num = double3::dot(a, bxc);
-      double denom = alen * blen * clen + double3::dot(a, b) * clen + double3::dot(a, c) * blen +
-                     double3::dot(b, c) * alen;
+      double alen = length(a);
+      double blen = length(b);
+      double clen = length(c);
+      double3 bxc = cross_high_precision(b, c);
+      double num = dot(a, bxc);
+      double denom = alen * blen * clen + dot(a, b) * clen + dot(a, c) * blen + dot(b, c) * alen;
       if (denom == 0.0) {
         if (dbg_level > 0) {
           std::cout << "denom == 0, skipping this tri\n";
@@ -2569,7 +2568,7 @@ static Array<Face *> triangulate_poly(Face *f, IMeshArena *arena)
     f->populate_plane(false);
   }
   const double3 &poly_normal = f->plane->norm;
-  int axis = double3::dominant_axis(poly_normal);
+  int axis = dominant_axis(poly_normal);
   /* If project down y axis as opposed to x or z, the orientation
    * of the polygon will be reversed.
    * Yet another reversal happens if the poly normal in the dominant
@@ -2783,7 +2782,7 @@ static void init_face_merge_state(FaceMergeState *fms,
       std::cout << "process tri = " << &tri << "\n";
     }
     BLI_assert(tri.plane_populated());
-    if (double3::dot(norm, tri.plane->norm) <= 0.0) {
+    if (dot(norm, tri.plane->norm) <= 0.0) {
       if (dbg_level > 0) {
         std::cout << "triangle has wrong orientation, skipping\n";
       }
@@ -2808,7 +2807,7 @@ static void init_face_merge_state(FaceMergeState *fms,
       }
       if (me_index == -1) {
         double3 vec = new_me.v2->co - new_me.v1->co;
-        new_me.len_squared = vec.length_squared();
+        new_me.len_squared = length_squared(vec);
         new_me.orig = tri.edge_orig[i];
         new_me.is_intersect = tri.is_intersect[i];
         new_me.dissolvable = (new_me.orig == NO_INDEX && !new_me.is_intersect);
@@ -3048,7 +3047,7 @@ static Vector<Face *> merge_tris_for_face(Vector<int> tris,
   bool done = false;
   double3 first_tri_normal = tm.face(tris[0])->plane->norm;
   double3 second_tri_normal = tm.face(tris[1])->plane->norm;
-  if (tris.size() == 2 && double3::dot(first_tri_normal, second_tri_normal) > 0.0) {
+  if (tris.size() == 2 && dot(first_tri_normal, second_tri_normal) > 0.0) {
     /* Is this a case where quad with one diagonal remained unchanged?
      * Worth special handling because this case will be very common. */
     Face &tri1 = *tm.face(tris[0]);
diff --git a/source/blender/blenlib/intern/mesh_intersect.cc b/source/blender/blenlib/intern/mesh_intersect.cc
index 85a6ab42013..04f692385c9 100644
--- a/source/blender/blenlib/intern/mesh_intersect.cc
+++ b/source/blender/blenlib/intern/mesh_intersect.cc
@@ -198,9 +198,9 @@ void Face::populate_plane(bool need_exact)
     else {
       mpq3 tr02 = vert[0]->co_exact - vert[2]->co_exact;
       mpq3 tr12 = vert[1]->co_exact - vert[2]->co_exact;
-      normal_exact = mpq3::cross(tr02, tr12);
+      normal_exact = cross(tr02, tr12);
     }
-    mpq_class d_exact = -mpq3::dot(normal_exact, vert[0]->co_exact);
+    mpq_class d_exact = -dot(normal_exact, vert[0]->co_exact);
     plane = new Plane(normal_exact, d_exact);
   }
   else {
@@ -215,9 +215,9 @@ void Face::populate_plane(bool need_exact)
     else {
       double3 tr02 = vert[0]->co - vert[2]->co;
       double3 tr12 = vert[1]->co - vert[2]->co;
-      normal = double3::cross_high_precision(tr02, tr12);
+      normal = cross_high_precision(tr02, tr12);
     }
-    double d = -double3::dot(normal, vert[0]->co);
+    double d = -dot(normal, vert[0]->co);
     plane = new Plane(normal, d);
   }
 }
@@ -1174,15 +1174,15 @@ static mpq2 project_3d_to_2d(const mpq3 &p3d, int proj_axis)
  */
 static double supremum_dot_cross(const double3 &a, const double3 &b)
 {
-  double3 abs_a = double3::abs(a);
-  double3 abs_b = double3::abs(b);
+  double3 abs_a = abs(a);
+  double3 abs_b = abs(b);
   double3 c;
   /* This is dot(cross(a, b), cross(a,b)) but using absolute values for a and b
    * and always using + when operation is + or -. */
   c[0] = abs_a[1] * abs_b[2] + abs_a[2] * abs_b[1];
   c[1] = abs_a[2] * abs_b[0] + abs_a[0] * abs_b[2];
   c[2] = abs_a[0] * abs_b[1] + abs_a[1] * abs_b[0];
-  return double3::dot(c, c);
+  return dot(c, c);
 }
 
 /* The index of dot when inputs are plane_coords with index 1 is much higher.
@@ -1219,11 +1219,11 @@ static int filter_plane_side(const double3 &p,
                              const double3 &abs_plane_p,
                              const double3 &abs_plane_no)
 {
-  double d = double3::dot(p - plane_p, plane_no);
+  double d = dot(p - plane_p, plane_no);
   if (d == 0.0) {
     return 0;
   }
-  double supremum = double3::dot(abs_p + abs_plane_p, abs_plane_no);
+  double supremum = dot(abs_p + abs_plane_p, abs_plane_no);
   double err_bound = supremum * index_plane_side * DBL_EPSILON;
   if (fabs(d) > err_bound) {
     return d > 0 ? 1 : -1;
@@ -1248,9 +1248,9 @@ static int filter_plane_side(const double3 &p,
 static inline mpq3 tti_interp(const mpq3 &a, const mpq3 &b, const mpq3 &c, const mpq3 &n)
 {
   mpq3 ab = a - b;
-  mpq_class den = mpq3::dot(ab, n);
+  mpq_class den = dot(ab, n);
   BLI_assert(den != 0);
-  mpq_class alpha = mpq3::dot(a - c, n) / den;
+  mpq_class alpha = dot(a - c, n) / den;
   return a - alpha * ab;
 }
 
@@ -1261,8 +1261,8 @@ static inline mpq3 tti_interp(const mpq3 &a, const mpq3 &b, const mpq3 &c, const
  */
 static inline int tti_above(const mpq3 &a, const mpq3 &b, const mpq3 &c, const mpq3 &ad)
 {
-  mpq3 n = mpq3::cross(b - a, c - a);
-  return sgn(mpq3::dot(ad, n));
+  mpq3 n = cross(b - a, c - a);
+  return sgn(dot(ad, n));
 }
 
 /**
@@ -1480,11 +1480,11 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   const double3 &d_r2 = vr2->co;
   const double3 &d_n2 = tri2.plane->norm;
 
-  const double3 &abs_d_p1 = double3::abs(d_p1);
-  const double3 &abs_d_q1 = double3::abs(d_q1);
-  const double3 &abs_d_r1 = double3::abs(d_r1);
-  const double3 &abs_d_r2 = double3::abs(d_r2);
-  const double3 &abs_d_n2 = double3::abs(d_n2);
+  const double3 &abs_d_p1 = abs(d_p1);
+  const double3 &abs_d_q1 = abs(d_q1);
+  const double3 &abs_d_r1 = abs(d_r1);
+  const double3 &abs_d_r2 = abs(d_r2);
+  const double3 &abs_d_n2 = abs(d_n2);
 
   int sp1 = filter_plane_side(d_p1, d_r2, d_n2, abs_d_p1, abs_d_r2, abs_d_n2);
   int sq1 = filter_plane_side(d_q1, d_r2, d_n2, abs_d_q1, abs_d_r2, abs_d_n2);
@@ -1500,9 +1500,9 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   }
 
   const double3 &d_n1 = tri1.plane->norm;
-  const double3 &abs_d_p2 = double3::abs(d_p2);
-  const double3 &abs_d_q2 = double3::abs(d_q2);
-  const double3 &abs_d_n1 = double3::abs(d_n1);
+  const double3 &abs_d_p2 = abs(d_p2);
+  const double3 &abs_d_q2 = abs(d_q2);
+  const double3 &abs_d_n1 = abs(d_n1);
 
   int sp2 = filter_plane_side(d_p2, d_r1, d_n1, abs_d_p2, abs_d_r1, abs_d_n1);
   int sq2 = filter_plane_side(d_q2, d_r1, d_n1, abs_d_q2, abs_d_r1, abs_d_n1);
@@ -1526,13 +1526,13 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
 
   const mpq3 &n2 = tri2.plane->norm_exact;
   if (sp1 == 0) {
-    sp1 = sgn(mpq3::dot(p1 - r2, n2));
+    sp1 = sgn(dot(p1 - r2, n2));
   }
   if (sq1 == 0) {
-    sq1 = sgn(mpq3::dot(q1 - r2, n2));
+    sq1 = sgn(dot(q1 - r2, n2));
   }
   if (sr1 == 0) {
-    sr1 = sgn(mpq3::dot(r1 - r2, n2));
+    sr1 = sgn(dot(r1 - r2, n2));
   }
 
   if (dbg_level > 1) {
@@ -1552,13 +1552,13 @@ static ITT_value intersect_tri_tri(const IMesh &tm, int t1, int t2)
   /* Repeat for signs of t2's vertices with respect to plane of t1. */
   const mpq3 &n1 = tri1.plane->norm_exact;
   if (sp2 == 0) {
-    sp2 = sgn(mpq3::dot(p2 - r1, n1));
+    sp2 = sgn(dot(p2 - r1, n1));
   }
   if (sq2 == 0) {
-    sq2 = sgn(mpq3::dot(q2 - r1, n1));
+    sq2 = sgn(dot(q2 - r1, n1));
   }
   if (sr2 == 0) {
-    sr2 = sgn(mpq3::dot(r2 - r1, n1));
+    sr2 = sgn(dot(r2 - r1, n1));
   }
 
   if (dbg_level > 1) {
@@ -1757,7 +1757,7 @@ static CDT_data prepare_cdt_input(const IMesh &tm, int t, const Vector<ITT_value
   BLI_assert(tm.face(t)->plane_populated());
   ans.t_plane = tm.face(t)->plane;
   BLI_assert(ans.t_plane->exact_populated());
-  ans.proj_axis = mpq3::dominant_axis(ans.t_plane->norm_exact);
+  ans.proj_axis = dominant_axis(ans.t_plane->norm_exact);
   prepare_need_tri(ans, tm, t);
   for (const ITT_value &itt : itts) {
     switch (itt.kind) {
@@ -1793,7 +1793,7 @@ static CDT_data prepare_cdt_input_for_cluster(const IMesh &tm,
   BLI_assert(tm.face(t0)->plane_populated());
   ans.t_plane = tm.face(t0)->plane;
   BLI_assert(ans.t_plane->exact_populated());
-  ans.proj_axis = mpq3::dominant_axis(ans.t_plane->norm_exact);
+  ans.proj_axis = dominant_axis(ans.t_plane->norm_exact);
   for (const int t : cl) {
     prepare_need_tri(ans, tm, t);
   }
@@ -2535,15 +2535,15 @@ static bool face_is_degenerate(const Face *f)
   }
   double3 da = v2->co - v0->co;
   double3 db = v2->co - v1->co;
-  double3 dab = double3::cross_high_precision(da, db);
-  double dab_length_squared = dab.length_squared();
+  double3 dab = cross_high_precision(da, db);
+  double dab_length_squared = length_squared(dab);
   double err_bound = supremum_dot_cross(dab, dab) * index_dot_cross * DBL_EPSILON;
   if (dab_length_squared > err_bound) {
     return false;
   }
   mpq3 a = v2->co_exact - v0->co_exact;
   mpq3 b = v2->co_exact - v1->co_exact;
-  mpq3 ab = mpq3::cross(a, b);
+  mpq3 ab = cross(a, b);
   if (ab.x == 0 && ab.y == 0 && ab.z == 0) {
     return true;
   }