# PhysicsMath > A set of mathematical operations that are useful for physics. These operations do not form a fully comprehensive mathematics library, they simply provide operations that are usually required when interacting with physics. ## Definition * **Type:** Struct * **Namespace:** [Unity.U2D.Physics](/engine/6000.6/script-reference/unity/u2d/physics.md) * **Assembly:** UnityEngine.PhysicsCore2DModule ```csharp public readonly struct PhysicsMath ``` ## Static Properties | Property | Description | | --------------------------------------------------------------------------- | ------------------------------------------------------------------------------------------------------------ | | [PI](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/pi.md) | Get the value of PI used internally by the physics system. Using this will help with determinism. | | [TAU](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/tau.md) | Get the value of tau (2 \* PI) used internally by the physics system. Using this will help with determinism. | ## Static Methods | Method | Description | | --------------------------------------------------------------------------------------------------------------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | [AngularVelocityToQuaternion](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/angularvelocitytoquaternion.md) | Calculate a [Quaternion](/engine/6000.6/script-reference/unityengine/quaternion.md) given a 2D angular velocity and a time to integrate over using the selected transform plane. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [Atan2](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/atan2.md) | Calculate the arc-tangent i.e. the angle of the provided slope y/x. This operates as deterministically as possible across platforms. | | [CosSin](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/cossin.md) | Calculate both the Cosine and Sine of the specified angle. | | [GetRelativeMatrix](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrelativematrix.md) | Get the relative transformation matrix between the two specified transforms using the specified transform plane. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [GetRelativeMatrix2D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrelativematrix2d.md) | Get the relative transformation matrix between the two specified transform matrix using the specified transform plane to transform into 2D space i.e. XY position and Z rotation. | | [GetRelativePose2D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrelativepose2d.md) | Get the relative transformation pose (translation, rotation and scale) between the two specified transform matrix using the specified transform plane to transform into 2D space. | | [GetRotationAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrotationaxes.md) | Get the used rotation axes, given the specified transform plane. This is the inverse of [PhysicsMath.GetRotationIgnoredAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrotationignoredaxes.md). If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [GetRotationIgnoredAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrotationignoredaxes.md) | Get the ignored rotation axes, given the specified transform plane. This is the inverse of [PhysicsMath.GetRotationAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/getrotationaxes.md). If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [GetTranslationAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/gettranslationaxes.md) | Get the used translation axes, given the specified transform plane. This is the inverse of [PhysicsMath.GetTranslationIgnoredAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/gettranslationignoredaxes.md). If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [GetTranslationIgnoredAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/gettranslationignoredaxes.md) | Get the ignored translation axes, given the specified transform plane. This is the inverse of [PhysicsMath.GetTranslationAxes](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/gettranslationaxes.md). If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [GetTranslationIgnoredAxis](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/gettranslationignoredaxis.md) | Get the ignored translation axis, given the specified transform plane. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [MaxAbsComponent](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/maxabscomponent.md) | Get the maximum absolute value component from the specified vector. | | [MinAbsComponent](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/minabscomponent.md) | Get the minimum absolute value component from the specified vector. | | [SetTransformFast2D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/settransformfast2d.md) | Set the Transform position and rotation using the specified [PhysicsWorld.TransformPlane](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane.md). For position, only two axis will be updated with the others remaining unchanged. For rotation, only a single rotation axis will be changed with the others set to zero. | | [SetTransformSlow3D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/settransformslow3d.md) | Set the Transform position and rotation using the specified [PhysicsWorld.TransformPlane](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane.md). For position, only two axis will be updated with the others remaining unchanged. For rotation, only a single rotation axis will be changed with the others remaining unchanged. | | [SpringDamper](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/springdamper.md) | Calculate a one-dimensional mass-spring-damper simulation which drives towards a zero translation. You can then compute the new position using: "translation += newSpeed \* deltaTime;" | | [Swizzle](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/swizzle.md) | Transform a Matrix position (with perspective divide) into a Matrix position using the selected transform plane. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [ToDegrees](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/todegrees.md) | Convert radians to degrees. This operates as deterministically as possible across platforms. See [PhysicsMath.ToRadians](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/toradians.md). | | [ToPhysicsTransform](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/tophysicstransform.md) | Transform a 3D [Transform](/engine/6000.6/script-reference/unityengine/transform.md) position and rotation to a 2D [PhysicsTransform](/engine/6000.6/script-reference/unity/u2d/physics/physicstransform.md). Scale is not part of a [PhysicsTransform](/engine/6000.6/script-reference/unity/u2d/physics/physicstransform.md) therefore it is ignored. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [ToPosition2D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/toposition2d.md) | Transform a 3D position into a 2D position using the selected transform plane. If TransformPlane.Custom is used then [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) is used. | | [ToPosition3D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/toposition3d.md) | Transform a 2D position into a 3D position using the selected transform plane. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [ToRadians](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/toradians.md) | Convert degrees to radians. This operates as deterministically as possible across platforms. See [PhysicsMath.ToDegrees](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/todegrees.md). | | [ToRotation2D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/torotation2d.md) | Transform a 3D rotation into a 2D angle using the selected transform plane. If TransformPlane.Custom is used then [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) is used. | | [ToRotationFast3D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/torotationfast3d.md) | Transform a 2D angle into a 3D rotation using the selected transform plane (Fast). The transformation is fast because the rotation is simplified by the fact that only a single axis of rotation is handled. All other axis rotations are reset to zero. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. | | [ToRotationSlow3D](/engine/6000.6/script-reference/unity/u2d/physics/physicsmath/torotationslow3d.md) | Transform a 2D angle into a 3D rotation using the selected transform plane (Slow). The transformation is slower because the rotation is more complex due to the fact that changing a single axis of rotation requires it to not affect any other axis rotations. If [PhysicsWorld.TransformPlane.Custom](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/custom.md) is used, [PhysicsWorld.TransformPlane.XY](/engine/6000.6/script-reference/unity/u2d/physics/physicsworld/transformplane/xy.md) will be used instead which may not provide the correct results. |