【UE5 C++】判断两点连线是否穿过球体

前言

原理

代码

测试

结果

前言

通过数学原理判断空间中任意两点的连线是否穿过球体，再通过射线检测检验算法的正确性。

原理

（1）设球体球心的坐标为 $O(C_{x},C_{y},C_{z})$ ，半径为r；

（2）设线段 $AB$ 中A点的坐标为 $A(x_{1},y_{1},z_{1})$ ，B点的坐标为 $B(x_{2},y_{2},z_{2})$

（3）计算 $\underset{OA}{\rightarrow}$ 、 $\underset{OB}{\rightarrow}$ 、 $\underset{AB}{\rightarrow}$

（4）计算点 $O$ 到线段 $AB$ 的最短距离 $d$

$d=\frac{|\underset{OA}{\rightarrow}\times \underset{AB}{\rightarrow}|}{|\underset{AB}{\rightarrow}|}$

(5) 如果 $d\leq r$ ，则线段 $AB$ 穿过球体；如果 $d> r$ ，则线段 $AB$ 不穿过球体。

代码

定义一个函数“IsCrossSphere”来判断线段 $AB$ 是否穿过球体，函数需要传入点A、B的坐标以及球心坐标和球体半径。

再定义一个结构体作为函数返回值

函数“IsCrossSphere”的实现如下

头文件：

// Fill out your copyright notice in the Description page of Project Settings.#pragma once#include "CoreMinimal.h"
#include "GameFramework/Actor.h"
#include "LineIsCrossSphere.generated.h"USTRUCT(BlueprintType)
struct FStruct_Result_IsLineCrossSphere
{GENERATED_BODY();
public:UPROPERTY(BlueprintReadWrite)float distanceOfLineAndSphereCenter;UPROPERTY(BlueprintReadWrite)bool isCrossSphere;
};UCLASS()
class STUDY_API ALineIsCrossSphere : public AActor
{GENERATED_BODY()public:	// Sets default values for this actor's propertiesALineIsCrossSphere();protected:// Called when the game starts or when spawnedvirtual void BeginPlay() override;UFUNCTION(BlueprintCallable)FStruct_Result_IsLineCrossSphere IsCrossSphere(FVector pointA, FVector pointB, FVector sphereOrginPoint, float sphereRadius);   //计算线段AB到球心的距离并判断AB是否穿过球体public:	// Called every framevirtual void Tick(float DeltaTime) override;};

源文件：

// Fill out your copyright notice in the Description page of Project Settings.#include "Test/LineIsCrossSphere.h"// Sets default values
ALineIsCrossSphere::ALineIsCrossSphere()
{// Set this actor to call Tick() every frame.  You can turn this off to improve performance if you don't need it.PrimaryActorTick.bCanEverTick = true;}// Called when the game starts or when spawned
void ALineIsCrossSphere::BeginPlay()
{Super::BeginPlay();}FStruct_Result_IsLineCrossSphere ALineIsCrossSphere::IsCrossSphere(FVector pointA, FVector pointB, FVector sphereOrginPoint, float sphereRadius)
{bool isCrossSphere;FVector OA = pointA - sphereOrginPoint;FVector OB = pointB - sphereOrginPoint;FVector AB = OB - OA;FVector n = OA.Cross(AB);float D = n.Size() / AB.Size();if (D > sphereRadius){isCrossSphere =  false;}else{isCrossSphere =  true;}FStruct_Result_IsLineCrossSphere result;result.isCrossSphere = isCrossSphere;result.distanceOfLineAndSphereCenter = D;return result;
}// Called every frame
void ALineIsCrossSphere::Tick(float DeltaTime)
{Super::Tick(DeltaTime);}