载入中...
搜索中...
未找到
eve::physics 命名空间参考

Optional physics backend for vehicle mobility and body attach. 更多...

命名空间

namespace  action_adapter
 
namespace  destruction_cook
 
namespace  detail
 
namespace  softbody
 
namespace  softbody_cook
 
namespace  trajectory
 

类

class  AcceleratorBackendProviderRegistration
 Move-only lifetime token for one independently registered accelerator provider. 更多...
 
class  Body
 2D rigid body (Box2D) in pixel-space coordinates. Owned by a World; create shapes with newRectangleFixture/newCircleFixture. 更多...
 
class  Body3D
 3D rigid body (Box3D) in meter-space coordinates (+Y up by convention). Owned by a World3D; create primitive or convex-hull shapes with the new*Shape APIs. 更多...
 
struct  BoneDetachEvent
 One ordered detach event emitted during step. 更多...
 
struct  BonePresentation
 Presentation snapshot for one bone (world pose + proxy extents). 更多...
 
struct  BroadPhaseAabb3D
 Fixed-capacity deterministic result of one AABB broad-phase query. 更多...
 
struct  BroadPhaseHit3D
 One generation-qualified shape returned by an owning broad-phase query. 更多...
 
struct  CameraSphereHit3D
 CameraSphereHit3D public API. 更多...
 
struct  CapsuleMove3D
 Owning result of continuous capsule movement. 更多...
 
struct  CapsuleMovePolicy3D
 Per-call capsule mover classification policy; never mutates persistent World3D settings. 更多...
 
struct  CapsuleOverlap3D
 Owning summary of a capsule overlap query. 更多...
 
class  Cloth
 Interactive 2D cloth — Verlet particles + distance constraints. Pixel space (same convention as Box2D World). Script-owned. 更多...
 
class  Cloth3D
 Interactive 3D cloth — Verlet particles + distance constraints. Meter space, +Y up, grid laid out in the XZ plane with the top row pinned. 更多...
 
struct  ClothContact3D
 Result of a 3D point probe: deepest non-sensor shape within radius. Normal points from the shape toward the probed point (meters). 更多...
 
class  ClothGPU
 GPU-accelerated 2D cloth — Verlet integration and distance-constraint relaxation run in a Vulkan compute shader; positions are read back each frame for drawing. Same pixel-space conventions and script API shape as Cloth. 更多...
 
class  ClothModel
 Reusable, validated cloth simulation asset. 更多...
 
struct  ClothModelDistanceConstraint
 Precomputed rest-length constraint between two cloth particles. 更多...
 
struct  ClothModelFoldConstraint
 Adjacent-triangle fold relationship around the shared edge (a,b). 更多...
 
struct  ClothModelParticle
 Immutable rest-space particle stored by a ClothModel. 更多...
 
struct  ClothModelTetherConstraint
 Geodesic maximum-distance constraint from a particle to a fixed anchor. 更多...
 
struct  ClothModelTriangle
 Triangle indices into a ClothModel particle array. 更多...
 
struct  ClusterBreakEvent
 Emitted when a broken edge separates two different cook clusters. 更多...
 
class  ContactRelay
 
class  Destruction
 Optional physics satellite for Chaos-style geometry-collection destruction. 更多...
 
struct  DestructionField
 One volumetric influence applied to a geometry-collection instance. 更多...
 
class  DestructionFx
 Optional presentation satellite for geometry-collection destruction. 更多...
 
struct  DestructionStepBudget
 Per-step production budgets (0 = unlimited). 更多...
 
struct  DestructionStepReceipt
 Observable outcome of one checked step. 更多...
 
class  DistanceField3D
 Regular 3D signed-distance grid for terrain and voxel collision queries. Negative samples are solid, positive samples are empty. Samples are stored at grid vertices and queried with trilinear interpolation. 更多...
 
struct  FieldApplicationReceipt
 Observable receipt for one checked field application. 更多...
 
class  Fixture
 2D fixture: a shape attached to a Body with material + filter settings. Also carries a string tag used by contact events. 更多...
 
class  Fluid2D
 Interactive 2D particle fluid (double-density relaxation) in pixel space. Script-owned; independent of Box2D World. 更多...
 
struct  FractureRecipe
 Versioned cook recipe for Chaos-style pre-fracture (schema v1). 更多...
 
struct  GeometryCollectionAsset
 Immutable cooked/authored geometry-collection asset. 更多...
 
struct  GeometryCollectionBone
 One pre-authored leaf bone (box collision proxy) inside a geometry collection. 更多...
 
struct  GeometryCollectionEdge
 One undirected structural edge with a strain break threshold. 更多...
 
class  GeometryCollectionInstance
 Runtime owner of bone state, connection strain, and PhysicsLink bindings. 更多...
 
struct  GeometryCollectionInstanceSnapshot
 Persistent runtime snapshot for one geometry-collection instance. 更多...
 
class  GeometryCollectionRenderer
 Presentation bridge for a borrowed geometry-collection instance. 更多...
 
class  IAcceleratorBackendProvider
 Optional provider that creates an accelerator backend for domain state. 更多...
 
class  ISimulationBackend
 Minimal observable contract for physics simulation providers. 更多...
 
class  Joint2D
 Script-facing Box2D joint owned by a World. 更多...
 
class  Joint3D
 Script-facing Box3D joint owned by a World3D. 更多...
 
class  Mechanism2D
 Composed 2D mechanical assembly owned by a World. 更多...
 
class  Mechanism3D
 Composed mechanical assembly owned by a World3D. 更多...
 
class  Physics
 Physics module — Box2D (2D) + Box3D (3D) rigid bodies and SPH fluid. Script: physics <- eve.Physics(); world <- physics.newWorld(0, 900); world3 <- physics.newWorld3D(0, -9.8, 0); 更多...
 
struct  PhysicsArtifactCollider
 Queryable CPU collider resource owned by the physics module. 更多...
 
struct  PhysicsArtifactHandleTag
 Owner tag for physics artifact runtime handles. 更多...
 
class  PhysicsArtifactProvider
 Real physics-module provider for generated collider publication. 更多...
 
struct  PhysicsArtifactRayHit
 Backend-neutral ray-query result used for parity tests. 更多...
 
class  PhysicsArtifactStage
 Staged, owning Box3D construction for one provider mutation. 更多...
 
struct  PhysicsBodyHandleTag
 Tag for a process-local physics-body handle. 更多...
 
struct  PhysicsJointHandleTag
 Tag for a process-local physics-joint handle. 更多...
 
struct  PhysicsJointLink
 Generation-qualified relationship between a World3D and one joint. 更多...
 
struct  PhysicsLink
 Generation-qualified relationship between one world and one body. 更多...
 
struct  PhysicsShapeHandleTag
 Tag for a process-local physics-shape handle. 更多...
 
struct  PhysicsShapeLink
 Generation-qualified relationship between a World3D and one shape. 更多...
 
struct  PhysicsVector3D
 Allocation-free owning three-dimensional physics value. 更多...
 
struct  PhysicsWorldHandleTag
 Tag for a process-local physics-world handle. 更多...
 
struct  QueryFilter3D
 Query filter applied atomically for one owning query operation. 更多...
 
struct  RayHit3D
 Owning snapshot of the closest ray intersection. 更多...
 
class  Rope
 Optional physics satellite that owns rope construction, schema, and script bindings. 更多...
 
class  Rope3D
 Renderer-independent particle rope with XPBD stretch and bend constraints. 更多...
 
struct  RopeColliderId
 Stable identifier for a rope-owned analytic collider. 更多...
 
class  Shape3D
 3D shape (box/sphere/capsule) attached to a Body3D with material settings. Created via Body3D::new*Shape; owned by the world. 更多...
 
struct  SimulationBackendSelection
 Result of choosing an optional accelerator or CPU alternate path. 更多...
 
struct  SimulationObservation
 Observable backend progress shared by CPU and accelerator providers. 更多...
 
struct  SimulationSettings
 Validated solver policy for one simulation step. 更多...
 
class  SoftBody3D
 Volumetric particle soft body using overlapping shape-matching clusters. 更多...
 
struct  SoftBody3DDefinition
 Versioned, owning creation definition for one volumetric soft body. 更多...
 
class  SoftBody3DRenderer
 Presentation-only renderer for a borrowed volumetric soft body. 更多...
 
struct  SoftBodyModel
 Backend-neutral, owning result of deterministic soft-body cooking. 更多...
 
struct  SoftBodyModelCluster
 An overlapping shape-matching cluster stored by particle index. 更多...
 
struct  SoftBodyModelDefinition
 Versioned authoring recipe used to cook a mesh-backed SoftBodyModel. 更多...
 
struct  SoftBodyModelParticle
 A particle stored in an immutable cooked soft-body model. 更多...
 
struct  SoftBodyModelSurfaceBinding
 A surface vertex bound directly to one cooked simulation particle. 更多...
 
class  TargetingLineOfSightAdapter
 Read-only 3D physics implementation of sensing's LOS capability. 更多...
 
class  TerrainLoadGravityState
 Caller-owned state for Pcg-style rigid-body activation after terrain loading. 更多...
 
class  World
 Box2D world wrapper (2D physics) with pixel-space coordinates. Handles stepping, gravity, raycasts, AABB queries and contact/impact events. 更多...
 
class  World3D
 Box3D rigid-body world. Script coordinates are meters (Box3D native), unlike 2D World which uses pixels + Physics.setMeter. 更多...
 
struct  WorldSnapshotAccess
 

类型定义

using PhysicsArtifactHandle = eve::RuntimeHandle< PhysicsArtifactHandleTag >
 Generation-qualified handle for a physics artifact collider.
 
using SimulationStep = eve::SimulationStep
 Compatibility alias for the common injected simulation step.
 
using SimulationStepCallback = void(*)(void *context, const eve::SimulationStep &step, const SimulationSettings &settings) noexcept
 Callback used by a domain-owned CPU or test backend adapter.
 
using PhysicsWorldHandle = eve::RuntimeHandle< PhysicsWorldHandleTag >
 Generation-qualified runtime identity for a physics world.
 
using PhysicsBodyHandle = eve::RuntimeHandle< PhysicsBodyHandleTag >
 Generation-qualified runtime identity for a physics body.
 
using PhysicsShapeHandle = eve::RuntimeHandle< PhysicsShapeHandleTag >
 Generation-qualified runtime identity for a physics shape.
 
using PhysicsJointHandle = eve::RuntimeHandle< PhysicsJointHandleTag >
 Generation-qualified runtime identity for a physics joint.
 

枚举

enum class  SimulationBackendKind { Cpu , Gpu , MockAccelerator }
 Kind of implementation that owns a simulation step. 更多...
 
enum class  SimulationBackendDomain {
  World2D , World3D , Cloth2D , Cloth3D ,
  Rope3D , SoftBody3D , SurfaceFluid
}
 Domain state consumed by an accelerator provider. 更多...
 
enum class  SimulationDeterminism { BitExact , ToleranceBounded , ExplicitlyNondeterministic }
 Determinism guarantee made by a simulation backend. 更多...
 
enum class  ClothConstraintKind : uint8_t { Structural , Shear , Bend }
 Type of a precomputed distance constraint in a cloth model. 更多...
 
enum class  DestructionFieldKind : std::uint8_t { Anchor = 0 , Strain = 1 , Impulse = 2 , Sleep = 3 }
 Runtime field kinds mirrored from Chaos Destruction Fields. 更多...
 
enum class  DestructionFieldFalloff : std::uint8_t { None = 0 , Linear = 1 }
 Falloff applied from the field centre to its radius. 更多...
 
enum class  FractureMode : std::uint8_t { UniformVoronoi = 0 , ClusteredVoronoi = 1 , Radial = 2 , Planar = 3 }
 Fracture pattern used when cooking a geometry collection. 更多...
 
enum class  BoneRuntimeState : std::uint8_t { Attached = 0 , Detached = 1 , Sleeping = 2 }
 Runtime lifecycle for one bone inside a geometry-collection instance. 更多...
 
enum class  RopeTopologyChange { Changed , Unchanged }
 Result of a topology-changing rope operation. 更多...
 
enum class  RopeColliderChange { Changed , Unchanged }
 Result of a rope collider mutation. 更多...
 
enum class  SoftBodySurfaceSampling { None , Vertices , Voxels }
 SoftBodySurfaceSampling public API. 更多...
 
enum class  SoftBodyVolumeSampling { None , Voxels }
 SoftBodyVolumeSampling public API. 更多...
 
enum class  ClothProbeStatus { Miss , Hit }
 Named outcome for a filtered cloth particle probe. 更多...
 

函数

PhysicsArtifactProvider & physicsArtifactProvider () noexcept
 Return the process-owned physics artifact provider singleton.
 
void registerPhysicsArtifactProvider ()
 Register the physics provider in the common capability registry.
 
constexpr std::string_view simulationBackendDomainName (SimulationBackendDomain domain) noexcept
 Returns the stable diagnostic spelling for an accelerated simulation domain.
 
constexpr std::string_view simulationBackendKindName (SimulationBackendKind kind) noexcept
 Returns the stable backend-kind spelling.
 
constexpr std::string_view simulationDeterminismName (SimulationDeterminism determinism) noexcept
 Returns the stable determinism-contract spelling.
 
std::ostream & operator<< (std::ostream &stream, SimulationBackendKind kind)
 Writes a backend kind for diagnostics.
 
std::ostream & operator<< (std::ostream &stream, SimulationDeterminism determinism)
 Writes a determinism contract for diagnostics.
 
 Module_IMPL (Destruction, new Destruction())
 
 Module_IMPL (DestructionFx, new DestructionFx())
 
 Module_IMPL (Physics, new Physics())
 
void registerPhysicsCapabilities ()
 Registers physics capabilities.
 
void registerCameraObstructionWorld (World3D *world)
 Registers camera obstruction world.
 
eve::Result< void > registerTargetingLineOfSightWorld (World3D *world)
 Registers a borrowed live World3D with the targeting LOS adapter.
 
 Module_IMPL (Rope, new Rope())
 
Result< void > beginTerrainLoadGravity (TerrainLoadGravityState *state, Body3D *body, bool terrainFound)
 Begin monitoring a body when a containing terrain scene exists.
 
Result< bool > advanceTerrainLoadGravity (TerrainLoadGravityState *state, Body3D *body, bool terrainLoaded, float deltaSeconds, float activationDelay)
 Advance terrain-load waiting and restore gravity after the configured delay.
 

详细描述

Optional physics backend for vehicle mobility and body attach.

载具模块数据模型:载具模板 / 命令 / 载具实体。

VehiclePhysics.cpp is compiled only when the physics module is enabled; VehiclePhysicsAbsent.cpp is compiled otherwise. Callers always link one of the two and must not include physics headers.

与引擎其他玩法模块一致(参考 card / weapon / rpg):组件是纯数据结构体, 行为放在 VehicleSystem(静态类)与 IVehicleMobility(可插拔移动模型)里。 载具可以声明武器挂点(MountDef),运行时由 Vehicle 模块通过 weapon 模块 创建 WeaponMountEntity 并挂载武器——RTS / 坦克 / FPS 的区别只体现在 命令队列 / 驾驶输入 / 座位(Phase 4)这些可选面上。

类型定义说明

◆ PhysicsArtifactHandle

Generation-qualified handle for a physics artifact collider.

在文件 ArtifactProvider.h 第 29 行定义.

◆ PhysicsBodyHandle

Generation-qualified runtime identity for a physics body.

在文件 PhysicsHandles.h 第 28 行定义.

◆ PhysicsJointHandle

Generation-qualified runtime identity for a physics joint.

在文件 PhysicsHandles.h 第 32 行定义.

◆ PhysicsShapeHandle

Generation-qualified runtime identity for a physics shape.

在文件 PhysicsHandles.h 第 30 行定义.

◆ PhysicsWorldHandle

Generation-qualified runtime identity for a physics world.

在文件 PhysicsHandles.h 第 26 行定义.

◆ SimulationStep

Compatibility alias for the common injected simulation step.

Physics does not define a second time value. eve::SimulationStep carries both the monotonically increasing persisted tick and the fixed duration.

在文件 SimulationBackend.h 第 111 行定义.

◆ SimulationStepCallback

using eve::physics::SimulationStepCallback = typedef void (*)(void* context, const eve::SimulationStep& step, const SimulationSettings& settings) noexcept

Callback used by a domain-owned CPU or test backend adapter.

在文件 SimulationBackend.h 第 300 行定义.

枚举类型说明

◆ BoneRuntimeState

enum class eve::physics::BoneRuntimeState : std::uint8_t
strong

Runtime lifecycle for one bone inside a geometry-collection instance.

枚举值
Attached 
Detached 
Sleeping 

在文件 GeometryCollectionInstance.h 第 20 行定义.

◆ ClothConstraintKind

enum class eve::physics::ClothConstraintKind : uint8_t
strong

Type of a precomputed distance constraint in a cloth model.

枚举值
Structural 
Shear 
Bend 

在文件 ClothModel.h 第 17 行定义.

◆ ClothProbeStatus

enum class eve::physics::ClothProbeStatus
strong

Named outcome for a filtered cloth particle probe.

枚举值
Miss 
Hit 

在文件 World3D.h 第 57 行定义.

◆ DestructionFieldFalloff

enum class eve::physics::DestructionFieldFalloff : std::uint8_t
strong

Falloff applied from the field centre to its radius.

枚举值
None 
Linear 

在文件 DestructionField.h 第 17 行定义.

◆ DestructionFieldKind

enum class eve::physics::DestructionFieldKind : std::uint8_t
strong

Runtime field kinds mirrored from Chaos Destruction Fields.

枚举值
Anchor 
Strain 
Impulse 
Sleep 

在文件 DestructionField.h 第 9 行定义.

◆ FractureMode

enum class eve::physics::FractureMode : std::uint8_t
strong

Fracture pattern used when cooking a geometry collection.

枚举值
UniformVoronoi 
ClusteredVoronoi 
Radial 
Planar 

在文件 FractureRecipe.h 第 16 行定义.

◆ RopeColliderChange

Result of a rope collider mutation.

枚举值
Changed 
Unchanged 

在文件 Rope3D.h 第 28 行定义.

◆ RopeTopologyChange

Result of a topology-changing rope operation.

枚举值
Changed 
Unchanged 

在文件 Rope3D.h 第 16 行定义.

◆ SimulationBackendDomain

Domain state consumed by an accelerator provider.

枚举值
World2D 
World3D 
Cloth2D 
Cloth3D 
Rope3D 
SoftBody3D 
SurfaceFluid 

在文件 SimulationBackend.h 第 39 行定义.

◆ SimulationBackendKind

Kind of implementation that owns a simulation step.

Gpu is reserved for a real accelerator provider. MockAccelerator is a provider used by contract tests and headless integrations; it deliberately has no graphics or device dependency.

枚举值
Cpu 
Gpu 
MockAccelerator 

在文件 SimulationBackend.h 第 32 行定义.

◆ SimulationDeterminism

Determinism guarantee made by a simulation backend.

枚举值
BitExact 

Same inputs produce identical bits under the declared runtime.

ToleranceBounded 

Results are equivalent within a documented numeric tolerance.

ExplicitlyNondeterministic 

Results may vary and are not suitable for replay equality.

在文件 SimulationBackend.h 第 64 行定义.

◆ SoftBodySurfaceSampling

SoftBodySurfaceSampling public API.

枚举值
None 
Vertices 
Voxels 

在文件 SoftBodyModelDefinition.h 第 16 行定义.

◆ SoftBodyVolumeSampling

SoftBodyVolumeSampling public API.

枚举值
None 
Voxels 

在文件 SoftBodyModelDefinition.h 第 18 行定义.

函数说明

◆ advanceTerrainLoadGravity()

EVENGINE_API_WORLD Result< bool > eve::physics::advanceTerrainLoadGravity ( TerrainLoadGravityState *  state,
Body3D *  body,
bool  terrainLoaded,
float  deltaSeconds,
float  activationDelay 
)

Advance terrain-load waiting and restore gravity after the configured delay.

参数
stateState initialized by beginTerrainLoadGravity.
bodyThe same live caller-owned body supplied at begin.
terrainLoadedCurrent regular terrain load state.
deltaSecondsInjected finite non-negative frame duration.
activationDelayFinite non-negative delay after the first loaded observation.
返回
True exactly once when gravity is restored and caller-owned components should activate. @ownership State and body remain caller-owned and are not retained. @thread Physics simulation owner thread only; no callbacks are invoked.

在文件 TerrainLoadGravity.cpp 第 28 行定义.

◆ beginTerrainLoadGravity()

EVENGINE_API_WORLD Result< void > eve::physics::beginTerrainLoadGravity ( TerrainLoadGravityState *  state,
Body3D *  body,
bool  terrainFound 
)

Begin monitoring a body when a containing terrain scene exists.

参数
stateRequired caller-owned state, initialized exactly once.
bodyRequired caller-owned dynamic body.
terrainFoundWhether the caller found a terrain scene containing the body.
返回
Success, or InvalidArgument before mutation. @ownership State and body remain caller-owned and are not retained. @thread Physics simulation owner thread only.

在文件 TerrainLoadGravity.cpp 第 10 行定义.

◆ Module_IMPL() [1/4]

eve::physics::Module_IMPL ( Destruction  ,
new   Destruction() 
)

◆ Module_IMPL() [2/4]

eve::physics::Module_IMPL ( DestructionFx  ,
new   DestructionFx() 
)

◆ Module_IMPL() [3/4]

eve::physics::Module_IMPL ( Physics  ,
new   Physics() 
)

◆ Module_IMPL() [4/4]

eve::physics::Module_IMPL ( Rope  ,
new   Rope() 
)

◆ operator<<() [1/2]

std::ostream & eve::physics::operator<< ( std::ostream &  stream,
SimulationBackendKind  kind 
)
inline

Writes a backend kind for diagnostics.

Simulation backend kind name.

在文件 SimulationBackend.h 第 94 行定义.

引用了 kind , 以及 simulationBackendKindName().

◆ operator<<() [2/2]

std::ostream & eve::physics::operator<< ( std::ostream &  stream,
SimulationDeterminism  determinism 
)
inline

Writes a determinism contract for diagnostics.

Simulation determinism name.

在文件 SimulationBackend.h 第 100 行定义.

引用了 simulationDeterminismName().

◆ physicsArtifactProvider()

EVENGINE_API_WORLD PhysicsArtifactProvider & eve::physics::physicsArtifactProvider ( )
noexcept

◆ registerCameraObstructionWorld()

void eve::physics::registerCameraObstructionWorld ( World3D *  world)

Registers camera obstruction world.

在文件 PhysicsCapabilities.cpp 第 177 行定义.

◆ registerPhysicsArtifactProvider()

EVENGINE_API_WORLD void eve::physics::registerPhysicsArtifactProvider ( )

Register the physics provider in the common capability registry.

Registers the backend-neutral generated-artifact collider provider.

在文件 ArtifactProvider.cpp 第 610 行定义.

引用了 physicsArtifactProvider().

被这些函数引用 registerPhysicsCapabilities().

◆ registerPhysicsCapabilities()

void eve::physics::registerPhysicsCapabilities ( )

Registers physics capabilities.

在文件 PhysicsCapabilities.cpp 第 158 行定义.

引用了 eve::sensing::ensureLineOfSightRouter(), impl, registerPhysicsArtifactProvider() , 以及 eve::sensing::World3D.

被这些函数引用 eve::physics::Physics::Physics().

◆ registerTargetingLineOfSightWorld()

eve::Result< void > eve::physics::registerTargetingLineOfSightWorld ( World3D *  world)

Registers a borrowed live World3D with the targeting LOS adapter.

参数
worldNon-null live World3D. Its lifetime is tracked weakly.
返回
Applied, NoOp for the same world, Conflict for another active world, or a structured failure for an invalid world.
注解
Synchronous simulation-thread operation.

在文件 PhysicsCapabilities.cpp 第 180 行定义.

引用了 world.

◆ simulationBackendDomainName()

constexpr std::string_view eve::physics::simulationBackendDomainName ( SimulationBackendDomain  domain)
constexprnoexcept

Returns the stable diagnostic spelling for an accelerated simulation domain.

在文件 SimulationBackend.h 第 50 行定义.

引用了 Cloth2D, Cloth3D, Rope3D, SoftBody3D, SurfaceFluid, World2D , 以及 World3D.

◆ simulationBackendKindName()

constexpr std::string_view eve::physics::simulationBackendKindName ( SimulationBackendKind  kind)
constexprnoexcept

Returns the stable backend-kind spelling.

在文件 SimulationBackend.h 第 74 行定义.

引用了 Cpu, Gpu, kind , 以及 MockAccelerator.

被这些函数引用 operator<<().

◆ simulationDeterminismName()

constexpr std::string_view eve::physics::simulationDeterminismName ( SimulationDeterminism  determinism)
constexprnoexcept

Returns the stable determinism-contract spelling.

在文件 SimulationBackend.h 第 84 行定义.

引用了 BitExact, ExplicitlyNondeterministic , 以及 ToleranceBounded.

被这些函数引用 operator<<().