2D triangle rasterizer
A triangle is defined by three sets of floating-point coordinates A pixel is defined as the product of two half-open sets [x,x+1)*[y,y+1) Thus any point is specifically inside one pixel
The aim of this rasterizer is to produce a VERY GOOD rasterization which is suitable for multiple purposes; thus, speed is less of a factor. Formally, instead of producing the set of pixels whose centers lie within the triangle, we produce a set of pixels which overlap the triangle AT ALL and, for each pixel, we produce a set of vertices which define the convex intersection of the pixel square and the triangle. This allows us to calculate the "correct" centroid-sampled position, calculate atlas masks, etc.
To ensure proper seaming between adjacent triangles, all edges are scan-converted from top to bottom.
Note: pixel coordinates are in usual "screen space" i.e. all coordinates positive, (0,0) is top-left
Classes
| Name | Description |
|---|---|
| Geo::RastFragment | stores a fragment of a triangle i.e. a triangle clipped to a pixel box |
| Geo::RastTri | records details of the input triangle |
| Geo::RastVert | stores a rasterization vertex, including barycentric coordinates |
Functions
| Name | Description |
|---|---|
| GetArea() | get signed area of fragment polygon; it's flipped if area < 0 |
| GetBarycentricCoords(float, float, float &, float &) | Gets the barycentric coords of the given point (x, y). |
| GetBarycentricCoords(float, float, float &, float &) | get barycentric coordinates of a point in the pixel |
| GetCentroid(RastVert &) | get centroid of fragment polygon (average of vertex positions) |
| IsPtInPoly(float, float) | is a given point in the fragment polygon? |
| RasterizeTriangle(float, float, float, float, float, float, RasterizationClient, void *) | rasterize a triangle |
| RasterizeWindingAgnosticTriangle(float, float, float, float, float, float, RasterizationClient, void *) | rasterize a triangle regardless of winding order |
| RastTri(float, float, float, float, float, float) | Constructor. |
| RastVert() | Constructors. |
| RastVert(float, float, float, float) | Constructors. |
Variables
| Name | Description |
|---|---|
| float m_dX2 | x2-x1, y2-y1 |
| float m_dX3 | x3-x1, y3-y1 |
| float m_dY2 | x2-x1, y2-y1 |
| float m_dY3 | x3-x1, y3-y1 |
| Geo::u32 m_NumPts | number of points in fragment polygon |
| const RastVert * m_Points | fragment polygon points; coordinates are in [0,1]x[0,1] i.e. |
| const RastTri * m_Tri | reference to triangle that owns this fragment |
| float m_U | Barycentric coordinates. |
| float m_V | Barycentric coordinates. |
| float m_X | Vertex position. |
| Geo::s32 m_X | integer coordinates of (top-left of) pixel |
| float m_X1 | x1, y1 |
| float m_Y | Vertex position. |
| Geo::s32 m_Y | integer coordinates of (top-left of) pixel |
| float m_Y1 | x1, y1 |
Typedefs
| Name | Description |
|---|---|
| void(* RasterizationClient)(const RastFragment *fragment, void *user) | callback function for rasterization |
| Anchor | ||||
|---|---|---|---|---|
|
float Geo::RastFragment::GetArea
...
public: float GetArea() const
...
get signed area of fragment polygon; it's flipped if area < 0
| Anchor | ||||
|---|---|---|---|---|
|
void Geo::RastTri::GetBarycentricCoords
...
public: void GetBarycentricCoords
(
float x,
float y,
float & u,
float & v
) const
...
Gets the barycentric coords of the given point (x, y).
| Anchor | ||||
|---|---|---|---|---|
|
void Geo::RastFragment::GetBarycentricCoords
...
public: void GetBarycentricCoords
(
float x,
float y,
float & u,
float & v
) const
...
get barycentric coordinates of a point in the pixel
| Anchor | ||||
|---|---|---|---|---|
|
void Geo::RastFragment::GetCentroid
...
public: void GetCentroid
(
RastVert & out
) const
...
get centroid of fragment polygon (average of vertex positions)
| Anchor | ||||
|---|---|---|---|---|
|
bool Geo::RastFragment::IsPtInPoly
...
public: bool IsPtInPoly
(
float x,
float y
) const
...
is a given point in the fragment polygon?
| Anchor | ||||
|---|---|---|---|---|
|
void Geo::RasterizeTriangle
...
public: void RasterizeTriangle
(
float x1,
float y1,
float x2,
float y2,
float x3,
float y3,
RasterizationClient emitter,
void * user
)
...
rasterize a triangle
| Anchor | ||||
|---|---|---|---|---|
|
void Geo::RasterizeWindingAgnosticTriangle
...
public: void RasterizeWindingAgnosticTriangle
(
float x1,
float y1,
float x2,
float y2,
float x3,
float y3,
RasterizationClient emitter,
void * user
)
...
rasterize a triangle regardless of winding order
| Anchor | ||||
|---|---|---|---|---|
|
Geo::RastTri::RastTri
...
public: RastTri
(
float x1,
float y1,
float x2,
float y2,
float x3,
float y3
)
...
Constructor.
| Anchor | ||||
|---|---|---|---|---|
|
Geo::RastVert::RastVert
...
public: RastVert()
...
Constructors.
| Anchor | ||||
|---|---|---|---|---|
|
Geo::RastVert::RastVert
...
public: RastVert
(
float x,
float y,
float u,
float v
)
...
Constructors.