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【UE5 C++】判断两点连线是否穿过球体

article 2024/12/2 11:00:03

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 properties
	ALineIsCrossSphere();

protected:
	// Called when the game starts or when spawned
	virtual 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 frame
	virtual 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);

}