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small3dlib/s3l.h
Miloslav Číž 0084e48b2c Add linear depth interpolation
2019-05-21 14:55:24 +02:00

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#ifndef S3L_H
#define S3L_H
/*
WIP
Simple realtime 3D software rasterization renderer. It is fast, focused on
resource-limited computers, located in a single C header file, with no
dependencies, using only integer arithmetics.
author: Miloslav Ciz
license: CC0 1.0 + additional waiver of all IP
--------------------
This work's goal is to never be encumbered by any exclusive intellectual
property rights. The work is therefore provided under CC0 1.0 + additional
WAIVER OF ALL INTELLECTUAL PROPERTY RIGHTS that waives the rest of
intellectual property rights not already waived by CC0 1.0. The WAIVER OF ALL
INTELLECTUAL PROPERTY RGHTS is as follows:
Each contributor to this work agrees that they waive any exclusive rights,
including but not limited to copyright, patents, trademark, trade dress,
industrial design, plant varieties and trade secrets, to any and all ideas,
concepts, processes, discoveries, improvements and inventions conceived,
discovered, made, designed, researched or developed by the contributor either
solely or jointly with others, which relate to this work or result from this
work. Should any waiver of such right be judged legally invalid or
ineffective under applicable law, the contributor hereby grants to each
affected person a royalty-free, non transferable, non sublicensable, non
exclusive, irrevocable and unconditional license to this right.
--------------------
CONVENTIONS:
This library should never draw pixels outside the specified screen
coordinates, so you don't have to check this!
Angles are in S3L_Units, a full angle (2 pi) is S3L_FRACTIONS_PER_UNITs.
We use row vectors.
In 3D space, a left-handed coord. system is used. One spatial unit is split
into S3L_FRACTIONS_PER_UNIT fractions (fixed point arithmetic).
y ^
| _
| /| z
| /
| /
[0,0,0]-------> x
Untransformed camera is placed at [0,0,0], looking forward along +z axis. The
projection plane is centered at [0,0,0], stretrinch from
-S3L_FRACTIONS_PER_UNIT to S3L_FRACTIONS_PER_UNIT horizontally (x),
vertical size (y) depends on the camera aspect ratio. Camera FOV is defined
by focal length.
y ^
| _
| /| z
____|_/__
| |/ |
-----[0,0,0]-|-----> x
|____|____|
|
|
Rotations use Euler angles and are generally in the extinsic Euler angles in
ZXY order (by Z, then by X, then by Y).
Coordinates of pixels on screen start typically at the top left, from [0,0].
Triangle rasterization rules are these (mostly same as OpenGL, D3D etc.):
- Let's define:
- left side:
- not exactly horizontal, and on the left side of triangle
- exactly horizontal and above the topmost
(in other words: its normal points at least a little to the left or
completely up)
- right side: not left side
- Pixel centers are at integer coordinates and triangle for drawing are
specified with integer coordinates of pixel centers.
- A pixel is rasterized:
- if its center is inside the triangle OR
- if its center is exactly on the triangle side which is left and at the
same time is not on the side that's right (case of a triangle that's on
a single line) OR
- if its center is exactly on the triangle corner of sides neither of which
is right.
These rules imply among others:
- Adjacent triangles don't have any overlapping pixels, nor gaps between.
- Triangles of points that lie on a single line are NOT rasterized.
- A single "long" triangle CAN be rasterized as non-continuous.
- Transforming (e.g. mirroring, rotating by 90 degrees etc.) a result of
rasterizing triangle A is NOT generally equal to applying the same
transformation to triangle A first and then rasterizing it. Even the number
of rasterized pixels is usually different.
- If specifying a triangle with integer coordinates, then:
- The bottom-most corner (or side) of a triangle is never rasterized
(because it is connected to a right side).
- The top-most corner can only be rasterized on completely horizontal side
(otherwise it is connected to a right side).
- Vertically middle corner is rasterized if and only if it is on the left
of the triangle and at the same time is also not the bottom-most corner.
*/
#include <stdint.h>
#ifndef S3L_RESOLUTION_X
#define S3L_RESOLUTION_X 640 ///< Redefine to your screen x resolution.
#endif
#ifndef S3L_RESOLUTION_Y
#define S3L_RESOLUTION_Y 480 ///< Redefine to your screen y resolution.
#endif
#ifndef S3L_COMPUTE_DEPTH
#define S3L_COMPUTE_DEPTH 0 /**< Whether to compute depth for each pixel
(fragment). Some other options may turn this
on. */
#endif
#ifndef S3L_PERSPECTIVE_CORRECTION
#define S3L_PERSPECTIVE_CORRECTION 0 /**< Specifies what type of perspective
correction (PC) to use. Remember
this is an expensive operation!
Possible values:
0: no PC, fastest but ugliest
1: full (per-pixel) PC, nicest but
extremely expensive!
2: triangle subdivided PC, a
compromise between quality and
speed (TODO, not implemented)
*/
#endif
typedef int32_t S3L_Unit; /**< Units of measurement in 3D space. There is
S3L_FRACTIONS_PER_UNIT in one spatial unit.
By dividing the unit into fractions we
effectively achieve fixed point arithmetic.
The number of fractions is a constant that
serves as 1.0 in floating point arithmetic
(normalization etc.). */
#define S3L_FRACTIONS_PER_UNIT 512 /**< How many fractions a spatial unit is
split into. WARNING: if setting
higher than 1024, you'll probably
have to modify a sin table otherwise
it will overflow. Also other things
may overflow, so rather don't do it. */
typedef int16_t S3L_ScreenCoord;
typedef uint16_t S3L_Index;
#ifndef S3L_NEAR
#define S3L_NEAR (S3L_FRACTIONS_PER_UNIT / 4) /**< Distance of the near
clipping plane. */
#endif
#ifndef S3L_FAST_LERP_QUALITY
#define S3L_FAST_LERP_QUALITY 8 /**< Quality (scaling) of SOME linear
interpolations. 0 will most likely be
faster, but artifacts can occur for
bigger tris, while higher values can fix
this -- in theory all higher values will
have the same speed (it is a shift
value), but it mustn't be too high to
prevent overflow. */
#endif
#define S3L_HALF_RESOLUTION_X (S3L_RESOLUTION_X >> 1)
#define S3L_HALF_RESOLUTION_Y (S3L_RESOLUTION_Y >> 1)
#define S3L_PROJECTION_PLANE_HEIGHT\
((S3L_RESOLUTION_Y * S3L_FRACTIONS_PER_UNIT * 2) / S3L_RESOLUTION_X)
/** Predefined vertices of a cube to simply insert in an array. These come with
S3L_CUBE_TRIANGLES and S3L_CUBE_TEXCOORDS. */
#define S3L_CUBE_VERTICES\
/* 0 front, bottom, right */\
S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 1 front, bottom, left */\
-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 2 front, top, right */\
S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 3 front, top, left */\
-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,\
/* 4 back, bottom, right */\
S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 5 back, bottom, left */\
-S3L_FRACTIONS_PER_UNIT/2,-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 6 back, top, right */\
S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,\
/* 7 back, top, left */\
-S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2,S3L_FRACTIONS_PER_UNIT/2
/** Predefined triangle indices of a cube, to be used with S3L_CUBE_VERTICES
and S3L_CUBE_TEXCOORDS. */
#define S3L_CUBE_TRIANGLES\
0, 3, 2, /* front */\
0, 1, 3,\
4, 0, 2, /* right */\
4, 2, 6,\
5, 4, 6, /* back */\
6, 7, 5,\
7, 3, 1, /* left */\
7, 1, 5,\
3, 6, 2, /* top */\
3, 7, 6,\
4, 1, 0, /* bottom */\
4, 5, 1
/** Predefined texture coordinates of a cube, corresponding to triangles (NOT
vertices), to be used with S3L_CUBE_VERTICES and S3L_CUBE_TRIANGLES. */
#define S3L_CUBE_TEXCOORDS(m)\
m,m, 0,0, m,0,\
m,m, 0,m, 0,0,\
m,0, m,m, 0,m,\
m,0, 0,m, 0,0,\
0,0, m,0, m,m,\
m,m, 0,m, 0,0,\
0,m, 0,0, m,0,\
0,m, m,0, m,m,\
m,m, 0,0, m,0,\
m,m, 0,m, 0,0,\
0,m, m,0, m,m,\
0,m, 0,0, m,0
/**
Vector that consists of four scalars and can represent homogenous
coordinates, but is generally also used as Vec3 and Vec2.
*/
typedef struct
{
S3L_Unit x;
S3L_Unit y;
S3L_Unit z;
S3L_Unit w;
} S3L_Vec4;
static inline void S3L_initVec4(S3L_Vec4 *v);
static inline void S3L_vec3Add(S3L_Vec4 *result, S3L_Vec4 added);
static inline void S3L_vec3Sub(S3L_Vec4 *result, S3L_Vec4 substracted);
#define S3L_writeVec4(v)\
printf("Vec4: %d %d %d %d\n",((v).x),((v).y),((v).z),((v).w))
typedef struct
{
S3L_Vec4 translation;
S3L_Vec4 rotation; /**< Euler angles. Rortation is applied in this order:
1. z = by z (roll) CW looking along z+
2. x = by x (pitch) CW looking along x+
3. y = by y (yaw) CW looking along y+ */
S3L_Vec4 scale;
} S3L_Transform3D;
static inline void S3L_initTransoform3D(S3L_Transform3D *t);
/** Converts rotation transformation to three direction vectors of given length
(any one can be NULL, in which case it won't be computed).
*/
void S3L_rotationToDirections(
S3L_Vec4 rotation,
S3L_Unit length,
S3L_Vec4 *forw,
S3L_Vec4 *right,
S3L_Vec4 *up);
typedef S3L_Unit S3L_Mat4[4][4]; /**< 4x4 matrix, used mostly for 3D
transforms. The indexing is this:
matrix[column][row]. */
#define S3L_writeMat4(m)\
printf("Mat4:\n %d %d %d %d\n %d %d %d %d\n %d %d %d %d\n %d %d %d %d\n"\
,(m)[0][0],(m)[1][0],(m)[2][0],(m)[3][0],\
(m)[0][1],(m)[1][1],(m)[2][1],(m)[3][1],\
(m)[0][2],(m)[1][2],(m)[2][2],(m)[3][2],\
(m)[0][3],(m)[1][3],(m)[2][3],(m)[3][3])
/** Initializes a 4x4 matrix to identity. */
static inline void S3L_initMat4(S3L_Mat4 *m);
void S3L_makeTranslationMat(
S3L_Unit offsetX,
S3L_Unit offsetY,
S3L_Unit offsetZ,
S3L_Mat4 *m);
/** Makes a scaling matrix. DON'T FORGET: scale of 1.0 is set with
S3L_FRACTIONS_PER_UNIT! */
void S3L_makeScaleMatrix(
S3L_Unit scaleX,
S3L_Unit scaleY,
S3L_Unit scaleZ,
S3L_Mat4 *m);
/** Makes a matrixfor rotation in the ZXY order. */
void S3L_makeRotationMatrixZXY(
S3L_Unit byX,
S3L_Unit byY,
S3L_Unit byZ,
S3L_Mat4 *m);
void S3L_makeRotationMatrixYXZ(
S3L_Unit byX,
S3L_Unit byY,
S3L_Unit byZ,
S3L_Mat4 *m);
void S3L_makeWorldMatrix(S3L_Transform3D worldTransform, S3L_Mat4 *m);
void S3L_makeCameraMatrix(S3L_Transform3D cameraTransform, S3L_Mat4 *m);
/** Multiplies a vector by a matrix with normalization by
S3L_FRACTIONS_PER_UNIT. Result is stored in the input vector. */
void S3L_vec4Xmat4(S3L_Vec4 *v, S3L_Mat4 *m);
/** Same as S3L_vec4Xmat4 but faster, because this version doesn't compute the
W component of the result, which is usually not needed. */
void S3L_vec3Xmat4(S3L_Vec4 *v, S3L_Mat4 *m);
/** Multiplies two matrices with normalization by S3L_FRACTIONS_PER_UNIT.
Result is stored in the first matrix. The result represents a transformation
that has the same effect as applying the transformation represented by m1 and
then m2 (in that order). */
void S3L_mat4Xmat4(S3L_Mat4 *m1, S3L_Mat4 *m2);
typedef struct
{
S3L_Unit focalLength; ///< Defines the field of view (FOV).
S3L_Transform3D transform;
} S3L_Camera;
static inline void S3L_initCamera(S3L_Camera *c);
typedef struct
{
S3L_ScreenCoord x; ///< Screen X coordinate.
S3L_ScreenCoord y; ///< Screen Y coordinate.
S3L_Unit barycentric0; /**< Barycentric coord 0 (corresponds to 1st vertex).
Together with 1 and 2 coords these serve to
locate the pixel on a triangle and interpolate
values between it's three points. The sum of the
three coordinates will always be exactly
S3L_FRACTIONS_PER_UNIT. */
S3L_Unit barycentric1; ///< Baryc. coord 1 (corresponds to 2nd vertex).
S3L_Unit barycentric2; ///< Baryc. coord 2 (corresponds to 3rd vertex).
S3L_Index triangleID;
S3L_Unit depth; ///< Depth (only if depth is turned on).
} S3L_PixelInfo; /**< Used to pass the info about a rasterized pixel
(fragment) to the user-defined drawing func. */
static inline void S3L_initPixelInfo(S3L_PixelInfo *p);
#define S3L_BACKFACE_CULLING_NONE 0
#define S3L_BACKFACE_CULLING_CW 1
#define S3L_BACKFACE_CULLING_CCW 2
#define S3L_MODE_TRIANGLES 0
#define S3L_MODE_LINES 1
#define S3L_MODE_POINTS 2
typedef struct
{
uint8_t backfaceCulling;
uint8_t mode;
} S3L_DrawConfig;
void S3L_initDrawConfig(S3L_DrawConfig *config);
// general helper functions
static inline S3L_Unit S3L_abs(S3L_Unit value);
static inline S3L_Unit S3L_min(S3L_Unit v1, S3L_Unit v2);
static inline S3L_Unit S3L_max(S3L_Unit v1, S3L_Unit v2);
static inline S3L_Unit S3L_wrap(S3L_Unit value, S3L_Unit mod);
static inline S3L_Unit S3L_nonZero(S3L_Unit value);
S3L_Unit S3L_sin(S3L_Unit x);
static inline S3L_Unit S3L_cos(S3L_Unit x);
/** Interpolated between two values, v1 and v2, in the same ratio as t is to
tMax. Does NOT prevent zero division. */
static inline S3L_Unit S3L_interpolate(
S3L_Unit v1,
S3L_Unit v2,
S3L_Unit t,
S3L_Unit tMax);
/** Same as S3L_interpolate but with v1 == 0. Should be faster. */
static inline S3L_Unit S3L_interpolateFrom0(
S3L_Unit v2,
S3L_Unit t,
S3L_Unit tMax);
/** Like S3L_interpolate, but uses a parameter that goes from 0 to
S3L_FRACTIONS_PER_UNIT - 1, which can be faster. */
static inline S3L_Unit S3L_interpolateByUnit(
S3L_Unit v1,
S3L_Unit v2,
S3L_Unit t);
/** Same as S3L_interpolateByUnit but with v1 == 0. Should be faster. */
static inline S3L_Unit S3L_interpolateByUnitFrom0(
S3L_Unit v2,
S3L_Unit t);
/** Returns a value interpolated between the three triangle vertices based on
barycentric coordinates. */
static inline S3L_Unit S3L_interpolateBarycentric(
S3L_Unit value0,
S3L_Unit value1,
S3L_Unit value2,
S3L_Unit barycentric0,
S3L_Unit barycentric1,
S3L_Unit barycentric2);
static inline void S3L_mapProjectionPlaneToScreen(
S3L_Vec4 point,
S3L_ScreenCoord *screenX,
S3L_ScreenCoord *screenY);
/** Draws a triangle according to given config. The vertices are specified in
projection-plane space (NOT screen space!) -- they wll be mapped to screen
space by thies function. If perspective correction is enabled, each vertex
has to have a depth (Z position in camera space) specified in the Z
component. */
void S3L_drawTriangle(
S3L_Vec4 point0,
S3L_Vec4 point1,
S3L_Vec4 point2,
const S3L_DrawConfig *config,
const S3L_Camera *camera,
S3L_Index triangleID);
static inline void S3L_rotate2DPoint(S3L_Unit *x, S3L_Unit *y, S3L_Unit angle);
//=============================================================================
// privates
#define S3L_COMPUTE_LERP_DEPTH\
(S3L_COMPUTE_DEPTH && (S3L_PERSPECTIVE_CORRECTION != 1))
#define S3L_SIN_TABLE_LENGTH 128
static const S3L_Unit S3L_sinTable[S3L_SIN_TABLE_LENGTH] =
{
/* 511 was chosen here as a highest number that doesn't overflow during
compilation for S3L_FRACTIONS_PER_UNIT == 1024 */
(0*S3L_FRACTIONS_PER_UNIT)/511, (6*S3L_FRACTIONS_PER_UNIT)/511,
(12*S3L_FRACTIONS_PER_UNIT)/511, (18*S3L_FRACTIONS_PER_UNIT)/511,
(25*S3L_FRACTIONS_PER_UNIT)/511, (31*S3L_FRACTIONS_PER_UNIT)/511,
(37*S3L_FRACTIONS_PER_UNIT)/511, (43*S3L_FRACTIONS_PER_UNIT)/511,
(50*S3L_FRACTIONS_PER_UNIT)/511, (56*S3L_FRACTIONS_PER_UNIT)/511,
(62*S3L_FRACTIONS_PER_UNIT)/511, (68*S3L_FRACTIONS_PER_UNIT)/511,
(74*S3L_FRACTIONS_PER_UNIT)/511, (81*S3L_FRACTIONS_PER_UNIT)/511,
(87*S3L_FRACTIONS_PER_UNIT)/511, (93*S3L_FRACTIONS_PER_UNIT)/511,
(99*S3L_FRACTIONS_PER_UNIT)/511, (105*S3L_FRACTIONS_PER_UNIT)/511,
(111*S3L_FRACTIONS_PER_UNIT)/511, (118*S3L_FRACTIONS_PER_UNIT)/511,
(124*S3L_FRACTIONS_PER_UNIT)/511, (130*S3L_FRACTIONS_PER_UNIT)/511,
(136*S3L_FRACTIONS_PER_UNIT)/511, (142*S3L_FRACTIONS_PER_UNIT)/511,
(148*S3L_FRACTIONS_PER_UNIT)/511, (154*S3L_FRACTIONS_PER_UNIT)/511,
(160*S3L_FRACTIONS_PER_UNIT)/511, (166*S3L_FRACTIONS_PER_UNIT)/511,
(172*S3L_FRACTIONS_PER_UNIT)/511, (178*S3L_FRACTIONS_PER_UNIT)/511,
(183*S3L_FRACTIONS_PER_UNIT)/511, (189*S3L_FRACTIONS_PER_UNIT)/511,
(195*S3L_FRACTIONS_PER_UNIT)/511, (201*S3L_FRACTIONS_PER_UNIT)/511,
(207*S3L_FRACTIONS_PER_UNIT)/511, (212*S3L_FRACTIONS_PER_UNIT)/511,
(218*S3L_FRACTIONS_PER_UNIT)/511, (224*S3L_FRACTIONS_PER_UNIT)/511,
(229*S3L_FRACTIONS_PER_UNIT)/511, (235*S3L_FRACTIONS_PER_UNIT)/511,
(240*S3L_FRACTIONS_PER_UNIT)/511, (246*S3L_FRACTIONS_PER_UNIT)/511,
(251*S3L_FRACTIONS_PER_UNIT)/511, (257*S3L_FRACTIONS_PER_UNIT)/511,
(262*S3L_FRACTIONS_PER_UNIT)/511, (268*S3L_FRACTIONS_PER_UNIT)/511,
(273*S3L_FRACTIONS_PER_UNIT)/511, (278*S3L_FRACTIONS_PER_UNIT)/511,
(283*S3L_FRACTIONS_PER_UNIT)/511, (289*S3L_FRACTIONS_PER_UNIT)/511,
(294*S3L_FRACTIONS_PER_UNIT)/511, (299*S3L_FRACTIONS_PER_UNIT)/511,
(304*S3L_FRACTIONS_PER_UNIT)/511, (309*S3L_FRACTIONS_PER_UNIT)/511,
(314*S3L_FRACTIONS_PER_UNIT)/511, (319*S3L_FRACTIONS_PER_UNIT)/511,
(324*S3L_FRACTIONS_PER_UNIT)/511, (328*S3L_FRACTIONS_PER_UNIT)/511,
(333*S3L_FRACTIONS_PER_UNIT)/511, (338*S3L_FRACTIONS_PER_UNIT)/511,
(343*S3L_FRACTIONS_PER_UNIT)/511, (347*S3L_FRACTIONS_PER_UNIT)/511,
(352*S3L_FRACTIONS_PER_UNIT)/511, (356*S3L_FRACTIONS_PER_UNIT)/511,
(361*S3L_FRACTIONS_PER_UNIT)/511, (365*S3L_FRACTIONS_PER_UNIT)/511,
(370*S3L_FRACTIONS_PER_UNIT)/511, (374*S3L_FRACTIONS_PER_UNIT)/511,
(378*S3L_FRACTIONS_PER_UNIT)/511, (382*S3L_FRACTIONS_PER_UNIT)/511,
(386*S3L_FRACTIONS_PER_UNIT)/511, (391*S3L_FRACTIONS_PER_UNIT)/511,
(395*S3L_FRACTIONS_PER_UNIT)/511, (398*S3L_FRACTIONS_PER_UNIT)/511,
(402*S3L_FRACTIONS_PER_UNIT)/511, (406*S3L_FRACTIONS_PER_UNIT)/511,
(410*S3L_FRACTIONS_PER_UNIT)/511, (414*S3L_FRACTIONS_PER_UNIT)/511,
(417*S3L_FRACTIONS_PER_UNIT)/511, (421*S3L_FRACTIONS_PER_UNIT)/511,
(424*S3L_FRACTIONS_PER_UNIT)/511, (428*S3L_FRACTIONS_PER_UNIT)/511,
(431*S3L_FRACTIONS_PER_UNIT)/511, (435*S3L_FRACTIONS_PER_UNIT)/511,
(438*S3L_FRACTIONS_PER_UNIT)/511, (441*S3L_FRACTIONS_PER_UNIT)/511,
(444*S3L_FRACTIONS_PER_UNIT)/511, (447*S3L_FRACTIONS_PER_UNIT)/511,
(450*S3L_FRACTIONS_PER_UNIT)/511, (453*S3L_FRACTIONS_PER_UNIT)/511,
(456*S3L_FRACTIONS_PER_UNIT)/511, (459*S3L_FRACTIONS_PER_UNIT)/511,
(461*S3L_FRACTIONS_PER_UNIT)/511, (464*S3L_FRACTIONS_PER_UNIT)/511,
(467*S3L_FRACTIONS_PER_UNIT)/511, (469*S3L_FRACTIONS_PER_UNIT)/511,
(472*S3L_FRACTIONS_PER_UNIT)/511, (474*S3L_FRACTIONS_PER_UNIT)/511,
(476*S3L_FRACTIONS_PER_UNIT)/511, (478*S3L_FRACTIONS_PER_UNIT)/511,
(481*S3L_FRACTIONS_PER_UNIT)/511, (483*S3L_FRACTIONS_PER_UNIT)/511,
(485*S3L_FRACTIONS_PER_UNIT)/511, (487*S3L_FRACTIONS_PER_UNIT)/511,
(488*S3L_FRACTIONS_PER_UNIT)/511, (490*S3L_FRACTIONS_PER_UNIT)/511,
(492*S3L_FRACTIONS_PER_UNIT)/511, (494*S3L_FRACTIONS_PER_UNIT)/511,
(495*S3L_FRACTIONS_PER_UNIT)/511, (497*S3L_FRACTIONS_PER_UNIT)/511,
(498*S3L_FRACTIONS_PER_UNIT)/511, (499*S3L_FRACTIONS_PER_UNIT)/511,
(501*S3L_FRACTIONS_PER_UNIT)/511, (502*S3L_FRACTIONS_PER_UNIT)/511,
(503*S3L_FRACTIONS_PER_UNIT)/511, (504*S3L_FRACTIONS_PER_UNIT)/511,
(505*S3L_FRACTIONS_PER_UNIT)/511, (506*S3L_FRACTIONS_PER_UNIT)/511,
(507*S3L_FRACTIONS_PER_UNIT)/511, (507*S3L_FRACTIONS_PER_UNIT)/511,
(508*S3L_FRACTIONS_PER_UNIT)/511, (509*S3L_FRACTIONS_PER_UNIT)/511,
(509*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511,
(510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511,
(510*S3L_FRACTIONS_PER_UNIT)/511, (510*S3L_FRACTIONS_PER_UNIT)/511
};
#define S3L_SIN_TABLE_UNIT_STEP\
(S3L_FRACTIONS_PER_UNIT / (S3L_SIN_TABLE_LENGTH * 4))
void S3L_initVec4(S3L_Vec4 *v)
{
v->x = 0; v->y = 0; v->z = 0; v->w = S3L_FRACTIONS_PER_UNIT;
}
void S3L_vec3Add(S3L_Vec4 *result, S3L_Vec4 added)
{
result->x += added.x;
result->y += added.y;
result->z += added.z;
}
void S3L_vec3Sub(S3L_Vec4 *result, S3L_Vec4 substracted)
{
result->x -= substracted.x;
result->y -= substracted.y;
result->z -= substracted.z;
}
void S3L_initMat4(S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = S; M(1,0) = 0; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = S; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = S; M(3,2) = 0;
M(0,3) = 0; M(1,3) = 0; M(2,3) = 0; M(3,3) = S;
#undef M
#undef S
}
void S3L_vec4Xmat4(S3L_Vec4 *v, S3L_Mat4 *m)
{
S3L_Vec4 vBackup;
vBackup.x = v->x;
vBackup.y = v->y;
vBackup.z = v->z;
vBackup.w = v->w;
// TODO: try alternative operation orders to optimize
#define dotCol(col)\
(vBackup.x * (*m)[col][0]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.y * (*m)[col][1]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.z * (*m)[col][2]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.w * (*m)[col][3]) / S3L_FRACTIONS_PER_UNIT
v->x = dotCol(0);
v->y = dotCol(1);
v->z = dotCol(2);
v->w = dotCol(3);
}
void S3L_vec3Xmat4(S3L_Vec4 *v, S3L_Mat4 *m)
{
S3L_Vec4 vBackup;
#undef dotCol
#define dotCol(col)\
(vBackup.x * (*m)[col][0]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.y * (*m)[col][1]) / S3L_FRACTIONS_PER_UNIT +\
(vBackup.z * (*m)[col][2]) / S3L_FRACTIONS_PER_UNIT +\
(*m)[col][3]
vBackup.x = v->x;
vBackup.y = v->y;
vBackup.z = v->z;
vBackup.w = v->w;
v->x = dotCol(0);
v->y = dotCol(1);
v->z = dotCol(2);
v->w = S3L_FRACTIONS_PER_UNIT;
}
#undef dotCol
S3L_Unit S3L_abs(S3L_Unit value)
{
return value >= 0 ? value : -1 * value;
}
S3L_Unit S3L_min(S3L_Unit v1, S3L_Unit v2)
{
return v1 >= v2 ? v2 : v1;
}
S3L_Unit S3L_max(S3L_Unit v1, S3L_Unit v2)
{
return v1 >= v2 ? v1 : v2;
}
S3L_Unit S3L_wrap(S3L_Unit value, S3L_Unit mod)
{
return value >= 0 ? (value % mod) : (mod + (value % mod) - 1);
}
S3L_Unit S3L_nonZero(S3L_Unit value)
{
return value != 0 ? value : 1;
}
S3L_Unit S3L_interpolate(S3L_Unit v1, S3L_Unit v2, S3L_Unit t, S3L_Unit tMax)
{
return v1 + ((v2 - v1) * t) / tMax;
}
S3L_Unit S3L_interpolateByUnit(S3L_Unit v1, S3L_Unit v2, S3L_Unit t)
{
return v1 + ((v2 - v1) * t) / S3L_FRACTIONS_PER_UNIT;
}
S3L_Unit S3L_interpolateByUnitFrom0(S3L_Unit v2, S3L_Unit t)
{
return (v2 * t) / S3L_FRACTIONS_PER_UNIT;
}
S3L_Unit S3L_interpolateFrom0(S3L_Unit v2, S3L_Unit t, S3L_Unit tMax)
{
return (v2 * t) / tMax;
}
void S3L_mat4Xmat4(S3L_Mat4 *m1, S3L_Mat4 *m2)
{
S3L_Mat4 mat1;
for (uint16_t row = 0; row < 4; ++row)
for (uint16_t col = 0; col < 4; ++col)
mat1[col][row] = (*m1)[col][row];
for (uint16_t row = 0; row < 4; ++row)
for (uint16_t col = 0; col < 4; ++col)
{
(*m1)[col][row] = 0;
for (uint16_t i = 0; i < 4; ++i)
(*m1)[col][row] +=
(mat1[i][row] * (*m2)[col][i]) / S3L_FRACTIONS_PER_UNIT;
}
}
S3L_Unit S3L_sin(S3L_Unit x)
{
x = S3L_wrap(x / S3L_SIN_TABLE_UNIT_STEP,S3L_SIN_TABLE_LENGTH * 4);
int8_t positive = 1;
if (x < S3L_SIN_TABLE_LENGTH)
x = x;
else if (x < S3L_SIN_TABLE_LENGTH * 2)
x = S3L_SIN_TABLE_LENGTH * 2 - x - 1;
else if (x < S3L_SIN_TABLE_LENGTH * 3)
{
x = x - S3L_SIN_TABLE_LENGTH * 2;
positive = 0;
}
else
{
x = S3L_SIN_TABLE_LENGTH - (x - S3L_SIN_TABLE_LENGTH * 3) - 1;
positive = 0;
}
return positive ? S3L_sinTable[x] : -1 * S3L_sinTable[x];
}
S3L_Unit S3L_cos(S3L_Unit x)
{
return S3L_sin(x - S3L_FRACTIONS_PER_UNIT / 4);
}
void S3L_makeTranslationMat(
S3L_Unit offsetX,
S3L_Unit offsetY,
S3L_Unit offsetZ,
S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = S; M(1,0) = 0; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = S; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = S; M(3,2) = 0;
M(0,3) = offsetX; M(1,3) = offsetY; M(2,3) = offsetZ; M(3,3) = S;
#undef M
#undef S
}
void S3L_makeScaleMatrix(
S3L_Unit scaleX,
S3L_Unit scaleY,
S3L_Unit scaleZ,
S3L_Mat4 *m)
{
#define M(x,y) (*m)[x][y]
M(0,0) = scaleX; M(1,0) = 0; M(2,0) = 0; M(3,0) = 0;
M(0,1) = 0; M(1,1) = scaleY; M(2,1) = 0; M(3,1) = 0;
M(0,2) = 0; M(1,2) = 0; M(2,2) = scaleZ; M(3,2) = 0;
M(0,3) = 0; M(1,3) = 0; M(2,3) = 0; M(3,3) = S3L_FRACTIONS_PER_UNIT;
#undef M
}
void S3L_makeRotationMatrixZXY(
S3L_Unit byX,
S3L_Unit byY,
S3L_Unit byZ,
S3L_Mat4 *m)
{
S3L_Unit sx = S3L_sin(byX);
S3L_Unit sy = S3L_sin(byY);
S3L_Unit sz = S3L_sin(byZ);
S3L_Unit cx = S3L_cos(byX);
S3L_Unit cy = S3L_cos(byY);
S3L_Unit cz = S3L_cos(byZ);
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = (cy * cz) / S + (sy * sx * sz) / (S * S);
M(1,0) = (cx * sz) / S;
M(2,0) = (cy * sx * sz) / (S * S) - (cz * sy) / S;
M(3,0) = 0;
M(0,1) = (cz * sy * sx) / (S * S) - (cy * sz) / S;
M(1,1) = (cx * cz) / S;
M(2,1) = (cy * cz * sx) / (S * S) + (sy * sz) / S;
M(3,1) = 0;
M(0,2) = (cx * sy) / S;
M(1,2) = -1 * sx;
M(2,2) = (cy * cx) / S;
M(3,2) = 0;
M(0,3) = 0;
M(1,3) = 0;
M(2,3) = 0;
M(3,3) = S3L_FRACTIONS_PER_UNIT;
#undef M
#undef S
}
void S3L_makeRotationMatrixYXZ(
S3L_Unit byX,
S3L_Unit byY,
S3L_Unit byZ,
S3L_Mat4 *m)
{
S3L_Unit sx = S3L_sin(byX);
S3L_Unit sy = S3L_sin(byY);
S3L_Unit sz = S3L_sin(byZ);
S3L_Unit cx = S3L_cos(byX);
S3L_Unit cy = S3L_cos(byY);
S3L_Unit cz = S3L_cos(byZ);
#define M(x,y) (*m)[x][y]
#define S S3L_FRACTIONS_PER_UNIT
M(0,0) = (cy * cz) / S - (sy * sx * sz) / (S * S);
M(1,0) = (cy * sz) / S + (sx * sy * cz) / (S * S);
M(2,0) = -1 * (cx * sy) / S;
M(3,0) = 0;
M(0,1) = -1 * (sz * cx) / S;
M(1,1) = (cz * cx) / S;
M(2,1) = sx;
M(3,1) = 0;
M(0,2) = (cz * sy) / S + (sz * sx * cy) / (S * S);
M(1,2) = (sz * sy) / S - (cz * sx * cy) / (S * S);
M(2,2) = (cx * cy) / S;
M(3,2) = 0;
M(0,3) = 0;
M(1,3) = 0;
M(2,3) = 0;
M(3,3) = S3L_FRACTIONS_PER_UNIT;
#undef M
#undef S
}
void S3L_initTransoform3D(S3L_Transform3D *t)
{
S3L_initVec4(&(t->translation));
S3L_initVec4(&(t->rotation));
t->scale.x = S3L_FRACTIONS_PER_UNIT;
t->scale.y = S3L_FRACTIONS_PER_UNIT;
t->scale.z = S3L_FRACTIONS_PER_UNIT;
}
void S3L_initCamera(S3L_Camera *c)
{
c->focalLength = S3L_FRACTIONS_PER_UNIT;
S3L_initTransoform3D(&(c->transform));
}
void S3L_rotationToDirections(
S3L_Vec4 rotation,
S3L_Unit length,
S3L_Vec4 *forw,
S3L_Vec4 *right,
S3L_Vec4 *up)
{
S3L_Mat4 m;
S3L_makeRotationMatrixZXY(-1 * rotation.x,-1 * rotation.y,-1 * rotation.z,&m);
if (forw != 0)
{
forw->x = 0;
forw->y = 0;
forw->z = length;
S3L_vec3Xmat4(forw,*m);
}
if (right != 0)
{
right->x = length;
right->y = 0;
right->z = 0;
S3L_vec3Xmat4(right,*m);
}
if (up != 0)
{
up->x = 0;
up->y = length;
up->z = 0;
S3L_vec3Xmat4(up,*m);
}
}
void S3L_initPixelInfo(S3L_PixelInfo *p) // TODO: maybe non-pointer for p
{ // could be faster?
p->x = 0;
p->y = 0;
p->barycentric0 = S3L_FRACTIONS_PER_UNIT;
p->barycentric1 = 0;
p->barycentric2 = 0;
p->triangleID = 0;
p->depth = 0;
}
void S3L_initDrawConfig(S3L_DrawConfig *config)
{
config->backfaceCulling = 1;
config->mode = S3L_MODE_TRIANGLES;
}
void S3L_PIXEL_FUNCTION(S3L_PixelInfo *pixel); // forward decl
// TODO: ^ should be inline?
typedef struct
{
int16_t steps;
int16_t err;
S3L_ScreenCoord x;
S3L_ScreenCoord y;
int16_t *majorCoord;
int16_t *minorCoord;
int16_t majorIncrement;
int16_t minorIncrement;
int16_t majorDiff;
int16_t minorDiff;
} S3L_BresenhamState; ///< State of drawing a line with Bresenham algorithm.
typedef struct
{
S3L_Unit valueScaled;
S3L_Unit stepScaled;
} S3L_FastLerpState;
#define S3L_getFastLerpValue(state)\
(state.valueScaled >> S3L_FAST_LERP_QUALITY)
#define S3L_stepFastLerp(state)\
state.valueScaled += state.stepScaled
typedef struct
{
S3L_ScreenCoord p0[2]; ///< 2D coordinates of the 1st point projection
S3L_ScreenCoord p1[2]; ///< 2D coordinates of the 2nd point projection
S3L_Unit a[3]; ///< 3D coordinates of the 1st projected point of the line
S3L_Unit b[3]; ///< 3D coordinates of the 2nd projected point of the line
S3L_Unit pointDifference[3]; ///< [bx - ax, by - ay, bz - cz]
S3L_ScreenCoord c[2]; /**< helper point to for a plane for the intersection
with line */
S3L_Unit fcx; ///< precomputed helper product
S3L_Unit fcy; ///< precomputed helper product
S3L_Unit focalLength;
} S3L_PerspectiveCorrectionState; ///< State for computing persp. correction.
/**
Initializes the state of perspective correction along a line. The correction
itself is then done using S3L_correctPerspective function, using the state.
*/
void S3L_initPerspectiveCorrectionState(
S3L_ScreenCoord x0,
S3L_ScreenCoord y0,
S3L_Unit depth0,
S3L_ScreenCoord x1,
S3L_ScreenCoord y1,
S3L_Unit depth1,
S3L_Unit focalLength,
S3L_PerspectiveCorrectionState *state)
{
state->focalLength = focalLength;
state->p0[0] = x0;
state->p0[1] = y0;
state->p1[0] = x1;
state->p1[1] = y1;
state->a[0] = (x0 * (depth0 + focalLength)) / focalLength;
state->a[1] = (y0 * (depth0 + focalLength)) / focalLength;
state->a[2] = depth0;
state->b[0] = (x1 * (depth1 + focalLength)) / focalLength;
state->b[1] = (y1 * (depth1 + focalLength)) / focalLength;
state->b[2] = depth1;
state->pointDifference[0] = state->b[0] - state->a[0];
state->pointDifference[1] = state->b[1] - state->a[1];
state->pointDifference[2] = state->b[2] - state->a[2];
state->c[0] = x1 + y1 - y0;
state->c[1] = y1 - x1 + x0;
state->fcx = focalLength * state->c[0];
state->fcy = focalLength * state->c[1];
}
S3L_Unit S3L_correctPerspective(
S3L_Unit interpolationParameter, S3L_PerspectiveCorrectionState *state)
{
S3L_Unit p[2]; // lin. interpolated position between the projections
// TODO: perhaps this could be interpolated faster by stepping?
p[0] =
S3L_interpolateByUnit(state->p0[0],state->p1[0],interpolationParameter);
p[1] =
S3L_interpolateByUnit(state->p0[1],state->p1[1],interpolationParameter);
S3L_Unit a, b, c, d; // plane coeficients
a = state->focalLength * p[1] - state->fcy;
b = state->fcx - state->focalLength * p[0];
c = p[0] * state->c[1] - p[1] * state->c[0];
d = state->focalLength * c;
a >>= 4; // TODO: this sometimes prevents overflow, but should be solved better!
b >>= 4;
c >>= 4;
d >>= 4;
S3L_Unit result =
(
- a * state->a[0] - b * state->a[1] - c * state->a[2] - d
)
/
S3L_nonZero(
(
a * state->pointDifference[0] +
b * state->pointDifference[1] +
c * state->pointDifference[2]
) / S3L_FRACTIONS_PER_UNIT
);
return result < 0 ? 0 :
(result > S3L_FRACTIONS_PER_UNIT ? S3L_FRACTIONS_PER_UNIT : result);
}
static inline S3L_Unit S3L_interpolateBarycentric(
S3L_Unit value0,
S3L_Unit value1,
S3L_Unit value2,
S3L_Unit barycentric0,
S3L_Unit barycentric1,
S3L_Unit barycentric2)
{
return
(
(value0 * barycentric0) +
(value1 * barycentric1) +
(value2 * barycentric2)
) / S3L_FRACTIONS_PER_UNIT;
}
void S3L_bresenhamInit(S3L_BresenhamState *state, int16_t x0, int16_t y0,
int16_t x1, int16_t y1)
{
int16_t dx = x1 - x0;
int16_t dy = y1 - y0;
int16_t absDx = S3L_abs(dx);
int16_t absDy = S3L_abs(dy);
if (absDx >= absDy)
{
state->majorCoord = &(state->x);
state->minorCoord = &(state->y);
state->minorDiff = 2 * absDy;
state->majorDiff = 2 * absDx;
state->err = 2 * dy - dx;
state->majorIncrement = dx >= 0 ? 1 : -1;
state->minorIncrement = dy >= 0 ? 1 : -1;
state->steps = absDx;
}
else
{
state->majorCoord = &(state->y);
state->minorCoord = &(state->x);
state->minorDiff = 2 * absDx;
state->majorDiff = 2 * absDy;
state->err = 2 * dx - dy;
state->majorIncrement = dy >= 0 ? 1 : -1;
state->minorIncrement = dx >= 0 ? 1 : -1;
state->steps = absDy;
}
state->x = x0;
state->y = y0;
}
int S3L_bresenhamStep(S3L_BresenhamState *state)
{
state->steps--;
(*state->majorCoord) += state->majorIncrement;
if (state->err > 0)
{
(*state->minorCoord) += state->minorIncrement;
state->err -= state->majorDiff;
}
state->err += state->minorDiff;
return state->steps >= 0;
}
void S3L_mapProjectionPlaneToScreen(
S3L_Vec4 point,
S3L_ScreenCoord *screenX,
S3L_ScreenCoord *screenY)
{
*screenX =
S3L_HALF_RESOLUTION_X +
(point.x * S3L_HALF_RESOLUTION_X) / S3L_FRACTIONS_PER_UNIT;
*screenY =
S3L_HALF_RESOLUTION_Y -
(point.y * S3L_HALF_RESOLUTION_X) / S3L_FRACTIONS_PER_UNIT;
}
void _S3L_drawFilledTriangle(
S3L_Vec4 point0,
S3L_Vec4 point1,
S3L_Vec4 point2,
const S3L_Camera *camera,
S3L_PixelInfo *p)
{
S3L_Vec4 *tPointPP, *lPointPP, *rPointPP; /* points in projction plane space
(in Units, normalized by
S3L_FRACTIONS_PER_UNIT) */
S3L_ScreenCoord x0, y0, x1, y1, x2, y2; /* points in screen space (pixel
coordinates) */
S3L_mapProjectionPlaneToScreen(point0,&x0,&y0);
S3L_mapProjectionPlaneToScreen(point1,&x1,&y1);
S3L_mapProjectionPlaneToScreen(point2,&x2,&y2);
S3L_ScreenCoord
tPointSx, tPointSy, // top point coords, in screen space
lPointSx, lPointSy, // left point coords, in screen space
rPointSx, rPointSy; // right point coords, in screen space
S3L_Unit *barycentric0; // bar. coord that gets higher from L to R
S3L_Unit *barycentric1; // bar. coord that gets higher from R to L
S3L_Unit *barycentric2; // bar. coord that gets higher from bottom up
// sort the points:
#define assignPoints(t,a,b)\
{\
tPointSx = x##t;\
tPointSy = y##t;\
tPointPP = &point##t;\
barycentric2 = &(p->barycentric##t);\
int16_t aDx = x##a - x##t;\
int16_t bDx = x##b - x##t;\
int16_t aDy = S3L_nonZero(y##a - y##t);\
int16_t bDy = S3L_nonZero(y##b - y##t);\
if ((aDx << 5) / aDy < (bDx << 5) / bDy)\
{\
lPointSx = x##a; lPointSy = y##a;\
rPointSx = x##b; rPointSy = y##b;\
lPointPP = &point##a; rPointPP = &point##b;\
barycentric0 = &(p->barycentric##b);\
barycentric1 = &(p->barycentric##a);\
}\
else\
{\
lPointSx = x##b; lPointSy = y##b;\
rPointSx = x##a; rPointSy = y##a;\
lPointPP = &point##b; rPointPP = &point##a;\
barycentric0 = &(p->barycentric##a);\
barycentric1 = &(p->barycentric##b);\
}\
}
if (y0 <= y1)
{
if (y0 <= y2)
assignPoints(0,1,2)
else
assignPoints(2,0,1)
}
else
{
if (y1 <= y2)
assignPoints(1,0,2)
else
assignPoints(2,0,1)
}
#undef assignPoints
// now draw the triangle line by line:
S3L_ScreenCoord splitY; // Y of the vertically middle point of the triangle
S3L_ScreenCoord endY; // bottom Y of the whole triangle
int splitOnLeft; /* whether splitY is the y coord. of left or right
point */
if (rPointSy <= lPointSy)
{
splitY = rPointSy;
splitOnLeft = 0;
endY = lPointSy;
}
else
{
splitY = lPointSy;
splitOnLeft = 1;
endY = rPointSy;
}
S3L_ScreenCoord currentY = tPointSy;
/* We'll be using an algorithm similar to Bresenham line algorithm. The
specifics of this algorithm are among others:
- drawing possibly a NON-CONTINUOUS line
- NOT tracing the line exactly, but rather rasterizing one the right
side of it, according to the pixel CENTERS, INCLUDING the pixel
centers
The principle is this:
- Move vertically by pixels and accumulate the error (abs(dx/dy)).
- If the error is greater than one (crossed the next pixel center), keep
moving horizontally and substracting 1 from the error until it is less
than 1 again.
- To make this INTEGER ONLY, scale the case so that distance between
pixels is equal to dy (instead of 1). This way the error becomes
dx/dy * dy == dx, and we're comparing the error to (and potentially
substracting) 1 * dy == dy. */
int16_t
/* triangle side:
left right */
lX, rX, // current x position on the screen
lDx, rDx, // dx (end point - start point)
lDy, rDy, // dy (end point - start point)
lInc, rInc, // direction in which to increment (1 or -1)
lErr, rErr, // current error (Bresenham)
lErrCmp, rErrCmp, // helper for deciding comparison (> vs >=)
lErrAdd, rErrAdd, // error value to add in each Bresenham cycle
lErrSub, rErrSub; // error value to substract when moving in x direction
S3L_FastLerpState lSideFLS, rSideFLS;
#if S3L_COMPUTE_LERP_DEPTH
S3L_FastLerpState lDepthFLS, rDepthFLS;
#define initDepthFLS(s,p1,p2)\
s##DepthFLS.valueScaled = p1##PointPP->z << S3L_FAST_LERP_QUALITY;\
s##DepthFLS.stepScaled = ((p2##PointPP->z << S3L_FAST_LERP_QUALITY) -\
s##DepthFLS.valueScaled) / (s##Dy != 0 ? s##Dy : 1);
#else
#define initDepthFLS(s,p1,p2) ;
#endif
/* init side for the algorithm, params:
s - which side (l or r)
p1 - point from (t, l or r)
p2 - point to (t, l or r)
down - whether the side coordinate goes top-down or vice versa */
#define initSide(s,p1,p2,down)\
s##X = p1##PointSx;\
s##Dx = p2##PointSx - p1##PointSx;\
s##Dy = p2##PointSy - p1##PointSy;\
initDepthFLS(s,p1,p2)\
s##SideFLS.stepScaled = (S3L_FRACTIONS_PER_UNIT << S3L_FAST_LERP_QUALITY)\
/ (s##Dy != 0 ? s##Dy : 1);\
s##SideFLS.valueScaled = 0;\
if (!down)\
{\
s##SideFLS.valueScaled = S3L_FRACTIONS_PER_UNIT << S3L_FAST_LERP_QUALITY;\
s##SideFLS.stepScaled *= -1;\
}\
s##Inc = s##Dx >= 0 ? 1 : -1;\
if (s##Dx < 0)\
{s##Err = 0; s##ErrCmp = 0;}\
else\
{s##Err = s##Dy; s##ErrCmp = 1;}\
s##ErrAdd = S3L_abs(s##Dx);\
s##ErrSub = s##Dy != 0 ? s##Dy : 1; /* don't allow 0, could lead to an
infinite substracting loop */
#define stepSide(s)\
while (s##Err - s##Dy >= s##ErrCmp)\
{\
s##X += s##Inc;\
s##Err -= s##ErrSub;\
}\
s##Err += s##ErrAdd;
initSide(r,t,r,1)
initSide(l,t,l,1)
#define initPC(f,t,pc)\
S3L_initPerspectiveCorrectionState(\
f##PointPP->x,\
f##PointPP->y,\
f##PointPP->z,\
t##PointPP->x,\
t##PointPP->y,\
t##PointPP->z,\
camera->focalLength,\
&pc##PC);
#if S3L_PERSPECTIVE_CORRECTION == 1
S3L_PerspectiveCorrectionState lPC, rPC, rowPC;
initPC(t,l,l)
initPC(t,r,r)
#endif
// clip to the screen in y dimension:
endY = S3L_min(endY,S3L_RESOLUTION_Y);
/* Clipping above the screen (y < 0) can't be easily done here, will be
handled inside the loop. */
while (currentY < endY) /* draw the triangle from top to bottom -- the
bottom-most row is left out because, following
from the rasterization rules (see top of the
source), it is to never be rasterized. */
{
if (currentY == splitY) // reached a vertical split of the triangle?
{
#define manageSplit(b0,b1,s)\
S3L_Unit *tmp = barycentric##b0;\
barycentric##b0 = barycentric##b1;\
barycentric##b1 = tmp;\
s##SideFLS.valueScaled = (S3L_FRACTIONS_PER_UNIT\
<< S3L_FAST_LERP_QUALITY) - s##SideFLS.valueScaled;\
s##SideFLS.stepScaled *= -1;
if (splitOnLeft)
{
initSide(l,l,r,0);
manageSplit(0,2,r)
#if S3L_PERSPECTIVE_CORRECTION == 1
initPC(r,l,l)
initPC(r,t,r)
#endif
}
else
{
initSide(r,r,l,0);
manageSplit(1,2,l)
#if S3L_PERSPECTIVE_CORRECTION == 1
initPC(l,r,r)
initPC(l,t,l)
#endif
}
}
stepSide(r)
stepSide(l)
if (currentY >= 0) /* clipping of pixels whose y < 0 (can't be easily done
outside the loop) */
{ /* TODO: ^ This is bad though, a single large
triangle outside he top of the screen will trigger
a long loop. Try to FIX THIS! */
p->y = currentY;
// draw the horizontal line
S3L_Unit rowLength = S3L_nonZero(rX - lX - 1); // prevent zero div
#if S3L_PERSPECTIVE_CORRECTION == 1
S3L_Unit
lDepth, rDepth,
lT, rT; // perspective-corrected position along either side
lT = S3L_correctPerspective(S3L_getFastLerpValue(lSideFLS),&lPC);
rT = S3L_correctPerspective(S3L_getFastLerpValue(rSideFLS),&rPC);
lDepth = S3L_interpolateByUnit(lPC.a[2],lPC.b[2],lT);
rDepth = S3L_interpolateByUnit(rPC.a[2],rPC.b[2],rT);
S3L_initPerspectiveCorrectionState(
S3L_interpolateByUnit(lPC.a[0],lPC.b[0],lT),
S3L_interpolateByUnit(lPC.a[1],lPC.b[1],lT),
lDepth,
S3L_interpolateByUnit(rPC.a[0],rPC.b[0],rT),
S3L_interpolateByUnit(rPC.a[1],rPC.b[1],rT),
rDepth,
camera->focalLength,
&rowPC
);
#else
S3L_FastLerpState b0FLS, b1FLS;
#if S3L_COMPUTE_LERP_DEPTH
S3L_FastLerpState depthFLS;
depthFLS.valueScaled = lDepthFLS.valueScaled;
depthFLS.stepScaled =
(rDepthFLS.valueScaled - lDepthFLS.valueScaled) / rowLength;
#endif
b0FLS.valueScaled = 0;
b1FLS.valueScaled = lSideFLS.valueScaled;
b0FLS.stepScaled = rSideFLS.valueScaled / rowLength;
b1FLS.stepScaled = -1 * lSideFLS.valueScaled / rowLength;
#endif
// clip to the screen in x dimension:
S3L_ScreenCoord rXClipped = S3L_min(rX,S3L_RESOLUTION_X),
lXClipped = lX;
if (lXClipped < 0)
{
lXClipped = 0;
#if S3L_PERSPECTIVE_CORRECTION != 1
b0FLS.valueScaled -= lX * b0FLS.stepScaled;
b1FLS.valueScaled -= lX * b1FLS.stepScaled;
#if S3L_COMPUTE_LERP_DEPTH
depthFLS.valueScaled -= lX * depthFLS.stepScaled;
#endif
#endif
}
// draw the row:
for (S3L_ScreenCoord x = lXClipped; x < rXClipped; ++x)
{
#if S3L_PERSPECTIVE_CORRECTION == 1
S3L_Unit rowT =
S3L_correctPerspective(S3L_interpolateFrom0(S3L_FRACTIONS_PER_UNIT,
x - lX,rowLength),&rowPC);
*barycentric0 =
S3L_interpolateByUnitFrom0(rT,rowT);
*barycentric1 =
S3L_interpolateByUnitFrom0(lT,S3L_FRACTIONS_PER_UNIT - rowT);
#else
*barycentric0 = S3L_getFastLerpValue(b0FLS);
*barycentric1 = S3L_getFastLerpValue(b1FLS);
S3L_stepFastLerp(b0FLS);
S3L_stepFastLerp(b1FLS);
#if S3L_COMPUTE_LERP_DEPTH
p->depth = S3L_getFastLerpValue(depthFLS);
S3L_stepFastLerp(depthFLS);
#endif
#endif
*barycentric2 = S3L_FRACTIONS_PER_UNIT - *barycentric0 - *barycentric1;
p->x = x;
S3L_PIXEL_FUNCTION(p);
}
} // y clipping
S3L_stepFastLerp(lSideFLS);
S3L_stepFastLerp(rSideFLS);
#if S3L_COMPUTE_LERP_DEPTH
S3L_stepFastLerp(lDepthFLS);
S3L_stepFastLerp(rDepthFLS);
#endif
++currentY;
}
#undef manageSplit
#undef initPC
#undef initSide
#undef stepSide
}
void S3L_drawTriangle(
S3L_Vec4 point0,
S3L_Vec4 point1,
S3L_Vec4 point2,
const S3L_DrawConfig *config,
const S3L_Camera *camera,
S3L_Index triangleID)
{
#define clipTest(c,cmp,v)\
(point0.c cmp (v) && point1.c cmp (v) && point2.c cmp (v))
if ( // early clipping -- test if completely outside frustum
clipTest(z,<=,S3L_NEAR) ||
clipTest(x,<,-1 * S3L_FRACTIONS_PER_UNIT) ||
clipTest(x,>,S3L_FRACTIONS_PER_UNIT) ||
clipTest(y,<,-1 * S3L_PROJECTION_PLANE_HEIGHT / 2) ||
clipTest(y,>,S3L_PROJECTION_PLANE_HEIGHT / 2)
)
return; // completely behind the camera
if (config->backfaceCulling != S3L_BACKFACE_CULLING_NONE)
{
int32_t winding = // determines CW or CCW
(
(point1.y - point0.y) * (point2.x - point1.x) -
(point1.x - point0.x) * (point2.y - point1.y)
);
if ((config->backfaceCulling == S3L_BACKFACE_CULLING_CW && winding < 0) ||
(config->backfaceCulling == S3L_BACKFACE_CULLING_CCW && winding >= 0))
return;
}
S3L_PixelInfo p;
S3L_initPixelInfo(&p);
p.triangleID = triangleID;
if (config->mode == S3L_MODE_TRIANGLES) // triangle mode
{
/* This function will perform the mapping to screen space itself, it needs
the original values, hence no conversion here. */
_S3L_drawFilledTriangle(point0,point1,point2,camera,&p);
return;
}
// map to screen space
S3L_ScreenCoord x0, y0, x1, y1, x2, y2;
S3L_mapProjectionPlaneToScreen(point0,&x0,&y0);
S3L_mapProjectionPlaneToScreen(point1,&x1,&y1);
S3L_mapProjectionPlaneToScreen(point2,&x2,&y2);
if (config->mode == S3L_MODE_LINES) // line mode
{
S3L_BresenhamState line;
S3L_Unit lineLen;
#define drawLine(p1,p2)\
S3L_bresenhamInit(&line,x##p1,y##p1,x##p2,y##p2);\
p.barycentric0 = 0;\
p.barycentric1 = 0;\
p.barycentric2 = 0;\
lineLen = S3L_nonZero(line.steps);\
do\
{\
if (line.x >= 0 && line.x < S3L_RESOLUTION_X &&\
line.y >= 0 && line.y < S3L_RESOLUTION_Y)\
{\
p.x = line.x; p.y = line.y;\
p.barycentric##p1 = S3L_interpolateFrom0(\
S3L_FRACTIONS_PER_UNIT,line.steps,lineLen); \
p.barycentric##p2 = S3L_FRACTIONS_PER_UNIT - p.barycentric##p1;\
S3L_PIXEL_FUNCTION(&p);\
}\
} while (S3L_bresenhamStep(&line));
drawLine(0,1)
drawLine(2,0)
drawLine(1,2)
#undef drawLine
}
else // point mode
{
if (x0 >= 0 && x0 < S3L_RESOLUTION_X && y0 >= 0 && y0 < S3L_RESOLUTION_Y)
{
p.x = x0; p.y = y0; p.barycentric0 = S3L_FRACTIONS_PER_UNIT;
p.barycentric1 = 0; p.barycentric2 = 0;
S3L_PIXEL_FUNCTION(&p);
}
if (x1 >= 0 && x1 < S3L_RESOLUTION_X && y1 >= 0 && y1 < S3L_RESOLUTION_Y)
{
p.x = x1; p.y = y1; p.barycentric0 = 0;
p.barycentric1 = S3L_FRACTIONS_PER_UNIT; p.barycentric2 = 0;
S3L_PIXEL_FUNCTION(&p);
}
if (x2 >= 0 && x2 < S3L_RESOLUTION_X && y2 >= 0 && y2 < S3L_RESOLUTION_Y)
{
p.x = x2; p.y = y2; p.barycentric0 = 0;
p.barycentric1 = 0; p.barycentric2 = S3L_FRACTIONS_PER_UNIT;
S3L_PIXEL_FUNCTION(&p);
}
}
}
void S3L_rotate2DPoint(S3L_Unit *x, S3L_Unit *y, S3L_Unit angle)
{
if (angle < S3L_SIN_TABLE_UNIT_STEP)
return; // no visible rotation
S3L_Unit angleSin = S3L_sin(angle);
S3L_Unit angleCos = S3L_cos(angle);
S3L_Unit xBackup = *x;
*x =
(angleCos * (*x)) / S3L_FRACTIONS_PER_UNIT -
(angleSin * (*y)) / S3L_FRACTIONS_PER_UNIT;
*y =
(angleSin * xBackup) / S3L_FRACTIONS_PER_UNIT +
(angleCos * (*y)) / S3L_FRACTIONS_PER_UNIT;
}
void S3L_makeWorldMatrix(S3L_Transform3D worldTransform, S3L_Mat4 *m)
{
S3L_makeScaleMatrix(
worldTransform.scale.x,
worldTransform.scale.y,
worldTransform.scale.z,
m
);
S3L_Mat4 t;
S3L_makeRotationMatrixZXY(
worldTransform.rotation.x,
worldTransform.rotation.y,
worldTransform.rotation.z,
&t);
S3L_mat4Xmat4(m,&t);
S3L_makeTranslationMat(
worldTransform.translation.x,
worldTransform.translation.y,
worldTransform.translation.z,
&t);
S3L_mat4Xmat4(m,&t);
}
void S3L_makeCameraMatrix(S3L_Transform3D cameraTransform, S3L_Mat4 *m)
{
S3L_makeTranslationMat(
-1 * cameraTransform.translation.x,
-1 * cameraTransform.translation.y,
-1 * cameraTransform.translation.z,
m);
S3L_Mat4 r;
S3L_makeRotationMatrixYXZ(
cameraTransform.rotation.x,
cameraTransform.rotation.y,
cameraTransform.rotation.z,
&r);
S3L_mat4Xmat4(m,&r);
}
static inline void S3L_perspectiveDivide(S3L_Vec4 *vector,
S3L_Unit focalLength)
{
S3L_Unit divisor = vector->z > 0 ? vector->z : (-1 * (vector->z - 1));
/* ^ This has two purposes:
1. Prevent division by zero.
2. Prevent a "rapid flip" of the vertex, e.g.: having a vertex
[100,0,0.1] z-divides it to [1000,0], but when it shift a short
distance to [100,0,-0.1], it z-divides to [-1000,0], rapidly flipping
from right to the left. */
vector->x = (vector->x * focalLength) / divisor;
vector->y = (vector->y * focalLength) / divisor;
}
void S3L_drawModelIndexed(
const S3L_Unit coords[],
const S3L_Index triangleVertexIndices[],
uint16_t triangleCount,
S3L_Transform3D modelTransform,
const S3L_Camera *camera,
const S3L_DrawConfig *config)
{
S3L_Index triangleIndex = 0;
S3L_Index coordIndex = 0;
S3L_Vec4 pointModel, transformed0, transformed1, transformed2;
S3L_Unit indexIndex = 0;
pointModel.w = S3L_FRACTIONS_PER_UNIT; // has to be "1.0" for translation
S3L_Mat4 mat1, mat2;
S3L_makeWorldMatrix(modelTransform,&mat1);
S3L_makeCameraMatrix(camera->transform,&mat2);
S3L_mat4Xmat4(&mat1,&mat2);
while (triangleIndex < triangleCount)
{
#define project(n)\
indexIndex = triangleVertexIndices[coordIndex] * 3;\
pointModel.x = coords[indexIndex];\
++indexIndex; /* TODO: put into square brackets? */\
pointModel.y = coords[indexIndex];\
++indexIndex;\
pointModel.z = coords[indexIndex];\
++coordIndex;\
S3L_vec3Xmat4(&pointModel,&mat1);\
transformed##n.x = pointModel.x;\
transformed##n.y = pointModel.y;\
transformed##n.z = pointModel.z;\
transformed##n.w = S3L_FRACTIONS_PER_UNIT;\
S3L_perspectiveDivide(&transformed##n,camera->focalLength);
/* TODO: maybe create an option that would use a cache here to not
transform the same point twice? */
project(0)
project(1)
project(2)
S3L_drawTriangle(transformed0,transformed1,transformed2,config,camera,
triangleIndex);
++triangleIndex;
}
}
#endif
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