**Note**: This form is for filling out answers for the 15-462/662 Fall 2020 midterm exam.  _You must put all your answers in this form, and submit it via Autolab_.  We will not accept photos/scans of written material, files sent via email, etc.  The formatting of this file must be preserved (e.g., do not change lines starting with hashmarks, or remove lines consisting of three backticks).  All code should be written in the provided (empty) functions.  Please also write your AndrewID below.

AndrewID:

## 1 (20 points) Getting Warmed Up

### 1a (6 points)

### 1b (7 points)

### 1c (7 points)

## 2 (40 points) Cubing the Sphere

### 2a (5 points)

```
Matrix4x4 bboxTransform( Vec3 c, // sphere center
                         double r ) // sphere radius
{

}
```

### 2b (6 points)


```
Vec3 interpolateWorldPosition(
      Vec3 p0, Vec3 p1, Vec3 p2, // vertex world coordinates
      Vec3 b ) // barycentric coordinates of sample point
{

}
```

### 2c (5 points)

```
double intersectSphere( Vec3 c, // center
                        double r, // radius
                        Vec3 o, // ray origin
                        Vec3 d ) // ray direction (unit)
{

}
```

### 2d (6 points)


```
void drawBBoxTriangle( Vec3 x0, Vec3 x1, Vec3 x2, // world coordinates
                       Vec2 u0, Vec2 u1, Vec2 u2, // projected coordinates
                       Vec3 c, double r, // sphere center/radius
                       double sphereColor,
                       double* depth, double* color, // buffers
                       int w, int h ) // buffer width/height
{

}
```

### 2e (6 points)

### 2f (6 points)

### 2g (6 points)

## 3 (40 points) Step Into the Shadow

### 3a (5 points)

### 3b (5 points)

### 3c (5 points)

```
bool onContour( Edge e, // edge to be tested
                Vec3 x // location of point light )
{

}
```

### 3d (5 points)

```
void shadowPolygon( Edge e, // contour edge
                    Vec3 x, // light position
                    Vec4& pi, Vec4& pj,  // endpoints along edge
                    Vec4& qi, Vec4& qj ) // endpoints at infinity
{

}
```

### 3e (5 points)

### 3f (5 points)

### 3g (5 points)

### 3h (5 points)

```
void drawShadowPolygon(
   Vec3 P0, Vec3 P1, Vec3 Q0, Vec3 Q1, // polygon vertices
   double* depth, double* stencil, double* color, // buffers
   int w, int h ) // buffer width/height
{

}
```