V2AS问路
【UE4】GAMES101 图形学作业5：光线与物体相交(球、三角面)
阅读原文时间：2021年10月25日阅读：5

  • 在这部分的课程中，我们将专注于使用光线追踪来渲染图像。在光线追踪中最重要的操作之一就是找到光线与物体的交点。一旦找到光线与物体的交点，就可以执行着色并返回像素颜色。

  • 在这次作业中，我们要实现两个部分：

    • 光线的生成
    • 光线与三角的相交。

  • 本次代码框架的工作流程为：

  • 效果

  • Render()

    • 主要在于将屏幕上的坐标，映射成从视源位置（相机位置）发出的射线

    • 像素位置映射到 [-1, 1]，注意上下颠倒问题

    • 主要代码

      void AActor_Assignment5::Render()
{
    FTexture2DMipMap& Mip = T_Result->PlatformData->Mips[0];
    FColor* Data = (FColor*)Mip.BulkData.Lock(LOCK_READ_ONLY);
      float scale = UKismetMathLibrary::DegTan(fov * 0.5f);
float imageAspectRatio = width / (float)height;

// Use this variable as the eye position to start your rays.
FVector eye_pos=cameraComp->GetComponentLocation();
int m = rowNumber * width;
for (int i = 0; i < width; ++i)
{
    // generate primary ray direction
    float pixelCenterX = (float)(i + 0.5f) / width;
    float pixelCenterY = (float)(rowNumber + 0.5f) / height;
      float x = (2 * pixelCenterX - 1) * imageAspectRatio * scale;
float y = (1- 2 * pixelCenterY) * scale; //轴颠倒       

FVector dir = FVector(1, x, y); // Don't forget to normalize this direction!
dir.Normalize();
FVector finalColor = castRay(eye_pos, dir, 0)*255;
framebuffer[m] = FColor(finalColor.X, finalColor.Y, finalColor.Z, 255);
//Data[(height - 1 - rowNumber) * width + i] = framebuffer[m];
Data[m] = framebuffer[m]; //texture Data
m++;
      }

Mip.BulkData.Unlock();
T_Result->UpdateResource();
rowNumber++;
if (m==width*height)
{
    bFinishedScan = true;
    TextureFromImgArr(framebuffer);
}
      }

  • rayTriangleIntersect()

    • 公式

    • 代码

      bool rayTriangleIntersect(const FVector& v0, const FVector& v1, const FVector& v2, const FVector& orig,
        const FVector& dir, float& tnear, float& u, float& v) const
{
    // TODO: Implement this function that tests whether the triangle
    // that's specified bt v0, v1 and v2 intersects with the ray (whose
    // origin is *orig* and direction is *dir*)
    // Also don't forget to update tnear, u and v.
    FVector E1 = v1 - v0;
    FVector E2 = v2 - v0;
    FVector S = orig - v0;
    FVector S1 = FVector::CrossProduct(dir, E2);
    FVector S2 = FVector::CrossProduct(S, E1);
      float factor = FVector::DotProduct(S1, E1);
float t = 1.0f / factor * FVector::DotProduct(S2, E2);
float b1 = 1.0f / factor * FVector::DotProduct(S1, S);
float b2 = 1.0f / factor * FVector::DotProduct(S2, dir);

if (t > 0 && b1 > 0 && b2 > 0 && (1 - b1 - b2) > 0) {
    tnear = t;
    u = b1;
    v = b2;
    return true;
}
return false;
      }

代码结构

  • AActor_Assignment5 测试入口及光线追踪主要函数，继承自AActor

    • BeginPlay() 初始化入口，调用InitialScene()
    • InitialScene() 初始化各种数据
    • Tick() 调用 Render()
    • Render() 按行进行光线扫描，更新 Texture
    • castRay() 计算光照和反射后的颜色
    • trace() 判断光线与物体是否相交
    • reflect() 计算反射方向
    • refract() 计算折射方向
    • fresnel() 计算菲涅尔系数
    • CreateTexture() 创建 Texture

  • AHw5_Shape 物体形状类，继承自AActor

    • intersect() 光线相交检测
    • getSurfaceProperties() 物体表面属性
    • evalDiffuseColor() 根据uv计算当前点的颜色
    • SetCenterAndRadius() 设置球心和半径

  • AHw5_Sphere 球形，继承自AHw5_Shape

    • intersect() 重写光线相交检测
    • getSurfaceProperties() 重写物体表面属性

  • AHw5_MeshTriangle 三角面构成的物体

    • intersect() 重写光线相交检测
    • getSurfaceProperties() 重写物体表面属性
    • evalDiffuseColor() 重写根据uv计算当前点的颜色
    • SetProperty() 设置三角面顶点、uv坐标数据等
    • DarwWireframe() 绘制线框

源码

  • Actor_Assignment5.h

    点击查看代码

    ```cpp
    #pragma once

    include "CoreMinimal.h"

    include "GameFramework/Actor.h"

    include "Hw5_Shape.h"

    include "Camera/CameraComponent.h"

    include "Components/BillboardComponent.h"

    include "Actor_Assignment5.generated.h"

    USTRUCT()

    struct FHit_payload

    {

    GENERATED_BODY()

    float tNear;

    uint32 index;

    FVector2D uv;

    AHw5_Shape* hit_obj;

    };

    UCLASS()

    class GAMES101_API AActor_Assignment5 : public AActor

    {

    GENERATED_BODY()

    public:

    // Sets default values for this actor's properties

    AActor_Assignment5();

    protected:

    // Called when the game starts or when spawned

    virtual void BeginPlay() override;

    public:

    // Called every frame

    virtual void Tick(float DeltaTime) override;

      void InitialScene();

  void Render();
  FVector castRay(const FVector& orig, const FVector& dir, int depth);
  TOptional<FHit_payload> trace(const FVector& orig, const FVector& dir);

  FVector reflect(const FVector& I, const FVector& N); //反射
  FVector refract(const FVector& I, const FVector& N, const float& ior); //折射
  float fresnel(const FVector& I, const FVector& N, const float& ior);

  void CreateTexture();

  void TextureFromImgArr(const TArray<FColor>& SrcData);

    public:

    UPROPERTY(EditAnywhere)

    int32 width = 128;

    UPROPERTY(EditAnywhere)

    int32 height = 96;

      float fov = 90;
  FVector backgroundColor = FVector(0.235294, 0.67451, 0.843137);

  UPROPERTY(EditAnywhere)
      int maxDepth = 5;
  float epsilon = 0.001; //本处偏移需要放大十倍，否则有噪点

  TArray<FVector> lights_pos;
  float lights_Intensity;

  UPROPERTY()
      TArray<AHw5_Shape*> objects;

  UPROPERTY(VisibleAnywhere)
      USceneComponent* rootComp;
  UPROPERTY(VisibleAnywhere)
      UCameraComponent* cameraComp;
  UPROPERTY(VisibleAnywhere)
      UBillboardComponent* light1;
  UPROPERTY(VisibleAnywhere)
      UBillboardComponent* light2;
  UPROPERTY(VisibleAnywhere,BlueprintReadWrite)
  UTexture2D* T_Result;

  bool bFinishedScan = false;
  int32 rowNumber = 0;

  UPROPERTY()
      TArray<FColor> framebuffer;

    };

    </details>

  • Actor_Assignment5.cpp

    点击查看代码

    ```cpp
    #include "Actor_Assignment5.h"
    #include "Hw5_Sphere.h"
    #include "Hw5_MeshTriangle.h"
    #include "Kismet/GameplayStatics.h"

    float kInfinity = TNumericLimits::Max();

    // Sets default values

    AActor_Assignment5::AActor_Assignment5()

    {

    // 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;

      rootComp = CreateDefaultSubobject<USceneComponent>(TEXT("rootComp"));
  SetRootComponent(rootComp);

  cameraComp = CreateDefaultSubobject<UCameraComponent>(TEXT("cameraComp"));
  cameraComp->SetupAttachment(rootComp);
  cameraComp->SetWorldLocation(FVector(-600, 0, 0));
  cameraComp->bCameraMeshHiddenInGame=false;

  light1 = CreateDefaultSubobject<UBillboardComponent>(TEXT("l1"));
  light2 = CreateDefaultSubobject<UBillboardComponent>(TEXT("l2"));
  light1->SetupAttachment(rootComp);
  light2->SetupAttachment(rootComp);
  light1->SetHiddenInGame(false);
  light2->SetHiddenInGame(false);
  static  ConstructorHelpers::FObjectFinder<UTexture2D> texAsset(TEXT("Texture2D'/Engine/EditorResources/LightIcons/S_LightDirectional.S_LightDirectional'"));
  if (texAsset.Succeeded()) {
      light1->SetSprite(texAsset.Object);
      light2->SetSprite(texAsset.Object);
  }

    }

    // Called when the game starts or when spawned

    void AActor_Assignment5::BeginPlay()

    {

    Super::BeginPlay();

      InitialScene();
  framebuffer.Init(FColor(0,0, 0, 255), width * height);
  CreateTexture();

    }

    // Called every frame

    void AActor_Assignment5::Tick(float DeltaTime)

    {

    Super::Tick(DeltaTime);

    if(!bFinishedScan)

    Render();

    }

    void AActor_Assignment5::InitialScene()

    {

    FTransform Spawntransform = FTransform(FRotator::ZeroRotator, FVector::ZeroVector);

    AHw5_Sphere* Sphere1 = GetWorld()->SpawnActorDeferred(AHw5_Sphere::StaticClass(), Spawntransform);

    if (Sphere1) {

    Sphere1->materialType = EMaterialType::DIFFUSE_AND_GLOSSY;

    Sphere1->diffuseColor = FVector(0.6, 0.7, 0.8);

    Sphere1->SetCenterAndRadius(FVector(4, -1, 0) * 50, 2 * 50);

    UGameplayStatics::FinishSpawningActor(Sphere1, Spawntransform);

    objects.Add(Sphere1);

    }

      AHw5_Sphere* Sphere2 = GetWorld()->SpawnActorDeferred<AHw5_Sphere>(AHw5_Sphere::StaticClass(), Spawntransform);
  if (Sphere2) {
      Sphere2->materialType = EMaterialType::REFLECTION_AND_REFRACTION;//REFLECTION_AND_REFRACTION;
      Sphere2->ior = 1.5;
      Sphere2->SetCenterAndRadius(FVector(0, 0.5, 0) * 50, 1.5 * 50);
      UGameplayStatics::FinishSpawningActor(Sphere2, Spawntransform);
      objects.Add(Sphere2);
  }

  Spawntransform = FTransform(FRotator::ZeroRotator, FVector::ZeroVector);
  AHw5_MeshTriangle* mesh = GetWorld()->SpawnActorDeferred<AHw5_MeshTriangle>(AHw5_MeshTriangle::StaticClass(), Spawntransform);
  if (mesh) {
      mesh->materialType = EMaterialType::DIFFUSE_AND_GLOSSY;
      TArray<FVector> verts = { {-3, 6,-3}, {9, 6,-3}, {9, -6, -3}, {-3, -6, -3} };
      for (auto& v : verts)
          v *= 50;
      TArray<uint32> vertIndex = { 0, 1, 3, 1, 2, 3 };
      TArray<FVector2D> st = { {0, 0}, {1, 0}, {1, 1}, {0, 1} };
      mesh->SetProperty(verts, vertIndex, 2, st);
      UGameplayStatics::FinishSpawningActor(mesh, Spawntransform);
      objects.Add(mesh);
  }

  lights_Intensity = 0.5  ;
  lights_pos.Add(FVector(-28, -20, 70) * 10);
  lights_pos.Add(FVector(4, 30, 50) * 10);
  light1->SetWorldLocation(lights_pos[0]);
  light2->SetWorldLocation(lights_pos[1]);

    }

    void AActor_Assignment5::Render()

    {

    FTexture2DMipMap& Mip = T_Result->PlatformData->Mips[0];

    FColor* Data = (FColor*)Mip.BulkData.Lock(LOCK_READ_ONLY);

      float scale = UKismetMathLibrary::DegTan(fov * 0.5f);
  float imageAspectRatio = width / (float)height;

  // Use this variable as the eye position to start your rays.
  FVector eye_pos=cameraComp->GetComponentLocation();
  int m = rowNumber * width;
  for (int i = 0; i < width; ++i)
  {
      // generate primary ray direction
      float pixelCenterX = (float)(i + 0.5f) / width;
      float pixelCenterY = (float)(rowNumber + 0.5f) / height;
      float x = (2 * pixelCenterX - 1) * imageAspectRatio * scale;
  float y = (1- 2 * pixelCenterY) * scale; //轴颠倒       

  FVector dir = FVector(1, x, y); // Don't forget to normalize this direction!
  dir.Normalize();
  FVector finalColor = castRay(eye_pos, dir, 0)*255;
  framebuffer[m] = FColor(finalColor.X, finalColor.Y, finalColor.Z, 255);
  //Data[(height - 1 - rowNumber) * width + i] = framebuffer[m];
  Data[m] = framebuffer[m]; //texture Data
  m++;
      }

  Mip.BulkData.Unlock();
  T_Result->UpdateResource();
  rowNumber++;
  if (m==width*height)
  {
      bFinishedScan = true;
      TextureFromImgArr(framebuffer);
  }

    }

    FVector AActor_Assignment5::castRay(const FVector& orig, const FVector& dir, int depth)

    {

    if (depth > maxDepth) {

    return FVector(0.0, 0.0, 0.0);

    }

      FVector hitColor = backgroundColor;
  auto payload = trace(orig, dir);
  if (payload.IsSet())
  {
      FVector hitPoint = orig + dir * payload->tNear;
      //UKismetSystemLibrary::DrawDebugPoint(GetWorld(), hitPoint, 1, FColor::Red, 20);
      UKismetSystemLibrary::DrawDebugLine(GetWorld(), orig, hitPoint, FColor(255,0,0,48), .02f, 1.0f);
      FVector N; // normal
  FVector2D st; // st coordinates
  payload-&gt;hit_obj-&gt;getSurfaceProperties(hitPoint, dir, payload-&gt;index, payload-&gt;uv, N, st);
  switch (payload-&gt;hit_obj-&gt;materialType) {
  case EMaterialType::REFLECTION_AND_REFRACTION:
  {
      FVector reflectionDirection = reflect(dir, N);
      FVector refractionDirection = refract(dir, N, payload-&gt;hit_obj-&gt;ior);
      FVector reflectionRayOrig = (FVector::DotProduct(reflectionDirection, N) &lt; 0) ?
          hitPoint - N * epsilon :
          hitPoint + N * epsilon;
      FVector refractionRayOrig = (FVector::DotProduct(refractionDirection, N) &lt; 0) ?
          hitPoint - N * epsilon :
          hitPoint + N * epsilon;

      FVector reflectionColor = castRay(reflectionRayOrig, reflectionDirection, depth + 1);
      FVector refractionColor=FVector::ZeroVector;
      if (reflectionDirection.Size() != 0)
          refractionColor = castRay(refractionRayOrig, refractionDirection, depth + 1);
      float kr = fresnel(dir, N, payload-&gt;hit_obj-&gt;ior);
      hitColor = reflectionColor * kr + refractionColor * (1 - kr);
      break
  }
  case EMaterialType::REFLECTION:
  {
      float kr = fresnel(dir, N, payload-&gt;hit_obj-&gt;ior);
      FVector reflectionDirection = reflect(dir, N);
      FVector reflectionRayOrig = (FVector::DotProduct(reflectionDirection, N) &lt; 0) ?
          hitPoint - N * epsilon :
          hitPoint + N * epsilon;
      hitColor = castRay(reflectionRayOrig, reflectionDirection, depth + 1) * kr;
      break;
  }
  default:
  {
      // [comment]
      // We use the Phong illumation model int the default case. The phong model
      // is composed of a diffuse and a specular reflection component.
      // [/comment]
      FVector lightAmt = FVector::ZeroVector, specularColor = FVector::ZeroVector;
      FVector shadowPointOrig = (FVector::DotProduct(dir, N) &lt; 0) ?
          hitPoint + N * epsilon :
          hitPoint - N * epsilon;
      // [comment]
      // Loop over all lights in the scene and sum their contribution up
      // We also apply the lambert cosine law
      // [/comment]
      for (auto&amp; light_position : lights_pos) {
          FVector lightDir = light_position - hitPoint;
          // square of the distance between hitPoint and the light
          float lightDistance2 = FVector::DotProduct(lightDir, lightDir);
          lightDir.Normalize();
          float LdotN = std::max(0.f, FVector::DotProduct(lightDir, N));
          // is the point in shadow, and is the nearest occluding object closer to the object than the light itself?
          auto shadow_res = trace(shadowPointOrig, lightDir);             

          bool inShadow = shadow_res.IsSet() &amp;&amp; (shadow_res-&gt;tNear * shadow_res-&gt;tNear &lt; lightDistance2);
          if(!inShadow)
              UKismetSystemLibrary::DrawDebugLine(GetWorld(), hitPoint, light_position, FColor(255,0,0,48), .02f, 1.0f);

          lightAmt += inShadow ? FVector::ZeroVector : lights_Intensity * LdotN* FVector::OneVector;
          FVector reflectionDirection = reflect(-lightDir, N);

          specularColor += powf(std::max(0.f, -FVector::DotProduct(reflectionDirection, dir)),
              payload-&gt;hit_obj-&gt;specularExponent) * lights_Intensity* FVector::OneVector;
      }

      hitColor = lightAmt * payload-&gt;hit_obj-&gt;evalDiffuseColor(st) * payload-&gt;hit_obj-&gt;Kd +specularColor * payload-&gt;hit_obj-&gt;Ks;
      break;
  }
  }
      }

  return hitColor;

    }

    TOptional AActor_Assignment5::trace(const FVector& orig, const FVector& dir)

    {

    float tNear = kInfinity;

    TOptional payload;

    for (const auto& object : objects)

    {

    float tNearK = kInfinity;

    uint32_t indexK;

    FVector2D uvK;

    if (object->intersect(orig, dir, tNearK, indexK, uvK) && tNearK <= tNear)

    {

    payload.Emplace();

    payload->hit_obj = object;

    payload->tNear = tNearK;

    payload->index = indexK;

    payload->uv = uvK;

    tNear = tNearK;

    }

    }

      return payload;

    }

    FVector AActor_Assignment5::reflect(const FVector& I, const FVector& N)

    {

    FVector res = I - 2 * FVector::DotProduct(I, N) * N;

    res.Normalize();

    return res;

    }

    FVector AActor_Assignment5::refract(const FVector& I, const FVector& N, const float& ior)

    {

    float cosi = UKismetMathLibrary::FClamp(FVector::DotProduct(I, N), -1, 1); //注意使用 FClamp

    float etai = 1, etat = ior;

    FVector n = N;

    if (cosi < 0) { cosi = -cosi; }

    else { std::swap(etai, etat); n = -N; }

    float eta = etai / etat;

    float k = 1 - eta * eta * (1 - cosi * cosi);

    FVector res = k < 0 ? FVector::ZeroVector : eta * I + (eta * cosi - sqrtf(k)) * n;

    res.Normalize();

    return res;

    }

    float AActor_Assignment5::fresnel(const FVector& I, const FVector& N, const float& ior)

    {

      float cosi = UKismetMathLibrary::FClamp(FVector::DotProduct(I, N), -1, 1);
  float etai = 1, etat = ior;
  if (cosi > 0) { std::swap(etai, etat); }
  // Compute sini using Snell's law
  float sint = etai / etat * sqrtf(std::max(0.f, 1 - cosi * cosi));
  // Total internal reflection
  if (sint >= 1) {
      return 1;
  }
  else {
      float cost = sqrtf(std::max(0.f, 1 - sint * sint));
      cosi = fabsf(cosi);
      float Rs = ((etat * cosi) - (etai * cost)) / ((etat * cosi) + (etai * cost));
      float Rp = ((etai * cosi) - (etat * cost)) / ((etai * cosi) + (etat * cost));
      return (Rs * Rs + Rp * Rp) / 2.0;
  }

    }

    void AActor_Assignment5::CreateTexture()

    {

    T_Result = UTexture2D::CreateTransient(width, height, PF_B8G8R8A8);

    T_Result->UpdateResource();

    FUpdateTextureRegion2D* RegionColor = new FUpdateTextureRegion2D(0, 0, 0, 0, width, height);

      T_Result->UpdateTextureRegions(
      (int32)0,
      (uint32)1,
      RegionColor,
      (uint32)(4 * 640),
      (uint32)4,
      (uint8*)framebuffer.GetData()
  );

    }

    void AActor_Assignment5::TextureFromImgArr(const TArray& SrcData)

    {

    const int32 SrcWidth = width;

    const int32 SrcHeight = height;

    // Create the texture

      //T_Result->ReleaseResource();
  // Lock the texture so it can be modified
  uint8* MipData = static_cast<uint8*>(T_Result->PlatformData->Mips[0].BulkData.Lock(LOCK_READ_WRITE));

  // Create base mip.
  uint8* DestPtr = NULL;
  const FColor* SrcPtr = NULL;
  for (int32 y = 0; y < SrcHeight; y++)
  {
      DestPtr = &MipData[(SrcHeight - 1 - y) * SrcWidth * sizeof(FColor)];
      SrcPtr = const_cast<FColor*>(&SrcData[(SrcHeight - 1 - y) * SrcWidth]);
      for (int32 x = 0; x < SrcWidth; x++)
      {
          *DestPtr++ = SrcData[SrcWidth * y + x].B;
          *DestPtr++ = SrcData[SrcWidth * y + x].G;
          *DestPtr++ = SrcData[SrcWidth * y + x].R;
          *DestPtr++ = 0xFF;
          SrcPtr++;
      }
  }

  // Unlock the texture
  T_Result->PlatformData->Mips[0].BulkData.Unlock();

  if (T_Result == nullptr)
      UKismetSystemLibrary::PrintString(GetWorld(), TEXT("T_Result is null"));

    }

        </details>

  • AHw5_Shape .h

    点击查看代码

    ```cpp
    #pragma once
    #include "CoreMinimal.h"
    #include "GameFramework/Actor.h"
    #include "Hw5_Shape.generated.h"

    UENUM(BlueprintType)

    enum class EMaterialType:uint8

    {

    DIFFUSE_AND_GLOSSY,

    REFLECTION_AND_REFRACTION,

    REFLECTION

    };

    UCLASS(Abstract)

    class GAMES101_API AHw5_Shape : public AActor

    {

    GENERATED_BODY()

    public:

    // Sets default values for this actor's properties

    AHw5_Shape()

    : materialType(EMaterialType::DIFFUSE_AND_GLOSSY)

    , ior(1.3)

    , Kd(0.8)

    , Ks(0.2)

    , diffuseColor(0.2)

    , specularExponent(25) {};

    public:

    virtual bool intersect(const FVector&, const FVector&, float&, uint32_t&, FVector2D&) const { return false; };

      virtual void getSurfaceProperties(const FVector&, const FVector&, const uint32_t&, const FVector2D&, FVector&,
      FVector2D&) const {};

  virtual FVector evalDiffuseColor(const FVector2D&) const
  {
      return diffuseColor;
  }

  // material properties
  EMaterialType materialType;
  float ior;
  float Kd, Ks;
  FVector diffuseColor;
  float specularExponent;

    };

        </details>

  • Hw5_Sphere.h

    点击查看代码

    ```cpp
    #include "CoreMinimal.h"
    #include
    #include "Hw5_Shape.h"
    #include "Kismet/KismetSystemLibrary.h"
    #include "Hw5_Sphere.generated.h"

    inline bool solveQuadratic(const float& a, const float& b, const float& c, float& x0, float& x1)

    {

    float discr = b * b - 4 * a * c;

    if (discr < 0)

    return false;

    else if (discr == 0)

    x0 = x1 = -0.5 * b / a;

    else

    {

    float q = (b > 0) ? -0.5 * (b + sqrt(discr)) : -0.5 * (b - sqrt(discr));

    x0 = q / a;

    x1 = c / q;

    }

    if (x0 > x1)

    std::swap(x0, x1);

    return true;

    }

    UCLASS()

    class GAMES101_API AHw5_Sphere : public AHw5_Shape

    {

    GENERATED_BODY()

    public:

    void SetCenterAndRadius(const FVector& c, const float& r) {

    center = c;

    radius = r;

    radius2 = r * r;

    UKismetSystemLibrary::DrawDebugSphere(GetWorld(), center, radius, 40.0f, FLinearColor::White, 3600, 1.0f);

    }

      bool intersect(const FVector& orig, const FVector& dir, float& tnear, uint32_t&, FVector2D&) const override
  {
      // analytic solution
      FVector L = orig - center;
      float a = FVector::DotProduct(dir, dir);
      float b = 2 * FVector::DotProduct(dir, L);
      float c = FVector::DotProduct(L, L) - radius2;
      float t0, t1;
      if (!solveQuadratic(a, b, c, t0, t1))
          return false;
      if (t0 < 0)
          t0 = t1;
      if (t0 < 0)
          return false;
      tnear = t0;
      return true;
      }

  void getSurfaceProperties(const FVector& P, const FVector&, const uint32_t&, const FVector2D&,
                            FVector& N, FVector2D&) const override
  {
      N = P - center;
      N.Normalize();
  }

    private:

    FVector center;

    float radius, radius2;

    };

        </details>

  • AHw5_MeshTriangle.h

    点击查看代码

    ```cpp
    #pragma once
    #include "CoreMinimal.h"
    #include "Hw5_Shape.h"
    #include "Kismet/KismetMathLibrary.h"
    #include "Kismet/KismetSystemLibrary.h"
    #include "Hw5_MeshTriangle.generated.h"

    UCLASS()

    class GAMES101_API AHw5_MeshTriangle : public AHw5_Shape

    {

    GENERATED_BODY()

    public:

    void DarwWireframe() {

    for (uint32_t k = 0; k < numTriangles; ++k)

    {

    const FVector& v0 = vertices[vertexIndex[k * 3]];

    const FVector& v1 = vertices[vertexIndex[k * 3 + 1]];

    const FVector& v2 = vertices[vertexIndex[k * 3 + 2]];

    UKismetSystemLibrary::DrawDebugLine(GetWorld(), v0, v1, FLinearColor::White, 3600, 2.0f);

    UKismetSystemLibrary::DrawDebugLine(GetWorld(), v1, v2, FLinearColor::White, 3600, 2.0f);

    UKismetSystemLibrary::DrawDebugLine(GetWorld(), v2, v0, FLinearColor::White, 3600, 2.0f);

    }

    }

    void SetProperty(const TArray& verts, const TArray& vertsIndex, const uint32_t& numTris, const TArray st)

    {

    vertices = verts;

    vertexIndex = vertsIndex;

    numTriangles = numTris;

    stCoordinates = st;

    DarwWireframe();

    }

      bool rayTriangleIntersect(const FVector& v0, const FVector& v1, const FVector& v2, const FVector& orig,
      const FVector& dir, float& tnear, float& u, float& v) const
  {
      // TODO: Implement this function that tests whether the triangle
      // that's specified bt v0, v1 and v2 intersects with the ray (whose
      // origin is *orig* and direction is *dir*)
      // Also don't forget to update tnear, u and v.
      FVector E1 = v1 - v0;
      FVector E2 = v2 - v0;
      FVector S = orig - v0;
      FVector S1 = FVector::CrossProduct(dir, E2);
      FVector S2 = FVector::CrossProduct(S, E1);
      float factor = FVector::DotProduct(S1, E1);
  float t = 1.0f / factor * FVector::DotProduct(S2, E2);
  float b1 = 1.0f / factor * FVector::DotProduct(S1, S);
  float b2 = 1.0f / factor * FVector::DotProduct(S2, dir);

  if (t &gt; 0 &amp;&amp; b1 &gt; 0 &amp;&amp; b2 &gt; 0 &amp;&amp; (1 - b1 - b2) &gt; 0) {
      tnear = t;
      u = b1;
      v = b2;
      return true;
  }
  return false;
      }

  bool intersect(const FVector& orig, const FVector& dir, float& tnear, uint32_t& index,
      FVector2D& uv) const override
  {
      bool intersect = false;
      for (uint32_t k = 0; k < numTriangles; ++k)
      {
          const FVector& v0 = vertices[vertexIndex[k * 3]];
          const FVector& v1 = vertices[vertexIndex[k * 3 + 1]];
          const FVector& v2 = vertices[vertexIndex[k * 3 + 2]];
          float t, u, v;
          if (rayTriangleIntersect(v0, v1, v2, orig, dir, t, u, v) && t < tnear)
          {
              tnear = t;
              uv.X = u;
              uv.Y = v;
              index = k;
              intersect |= true;
          }
      }
      return intersect;
  }

  void getSurfaceProperties(const FVector&, const FVector&, const uint32_t& index, const FVector2D& uv, FVector& N,
      FVector2D& st) const override
  {
      const FVector& v0 = vertices[vertexIndex[index * 3]];
      const FVector& v1 = vertices[vertexIndex[index * 3 + 1]];
      const FVector& v2 = vertices[vertexIndex[index * 3 + 2]];
      FVector e0 = v1 - v0;
      FVector e1 = v1 - v2; // 注意向量方向，v2 - v1 会造成法线方向反向
      e0.Normalize();
      e1.Normalize();
      N = FVector::CrossProduct(e0, e1);
      N.Normalize();
      const FVector2D& st0 = stCoordinates[vertexIndex[index * 3]];
      const FVector2D& st1 = stCoordinates[vertexIndex[index * 3 + 1]];
      const FVector2D& st2 = stCoordinates[vertexIndex[index * 3 + 2]];
      st = st0 * (1 - uv.X - uv.Y) + st1 * uv.X + st2 * uv.Y;
  }

  FVector evalDiffuseColor(const FVector2D& st) const override
  {
      float scale = 5;
      float pattern = (fmodf(st.X * scale, 1) > 0.5) ^ (fmodf(st.Y * scale, 1) > 0.5);
      return UKismetMathLibrary::VLerp(FVector(0.815, 0.235, 0.031), FVector(0.937, 0.937, 0.231), pattern);
  }

  UPROPERTY()
      TArray<FVector> vertices;
      uint32_t numTriangles;
      UPROPERTY()
      TArray<uint32> vertexIndex;
  UPROPERTY()
      TArray<FVector2D> stCoordinates;

    };

        </details>

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