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

float Geo::RastFragment::GetArea

public: float GetArea() const

get signed area of fragment polygon; it's flipped if area < 0

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).

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

void Geo::RastFragment::GetCentroid

public: void GetCentroid
(
RastVert & out
) const

get centroid of fragment polygon (average of vertex positions)

bool Geo::RastFragment::IsPtInPoly

public: bool IsPtInPoly
(
float x,
float y
) const

is a given point in the fragment polygon?

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

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

Geo::RastTri::RastTri

public: RastTri
(
float x1,
float y1,
float x2,
float y2,
float x3,
float y3
)

Constructor.

Geo::RastVert::RastVert

public: RastVert()

Constructors.

Geo::RastVert::RastVert

public: RastVert
(
float x,
float y,
float u,
float v
)

Constructors.