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import struct
import numpy as np
from enum import Enum, auto
from typing import List, Dict, Tuple, Optional
class Rasterizer:
def __init__(self, driver):
self.driver = driver
print("Rasterizer initialized.")
def _compute_edge_function(self, x0, y0, x1, y1, px, py):
"""
Compute edge function for point (px,py) against edge (x0,y0)->(x1,y1)
Positive value means point is on left side of edge
"""
return (px - x0) * (y1 - y0) - (py - y0) * (x1 - x0)
def _is_top_left_edge(self, x0, y0, x1, y1):
"""Check if edge is top or left edge for tie-breaking rules"""
return (y0 == y1 and x0 < x1) or y0 < y1
def _compute_perspective_w(self, barycentric, w0, w1, w2):
"""Compute perspective-correct interpolation weight"""
return 1.0 / (barycentric[0]/w0 + barycentric[1]/w1 + barycentric[2]/w2)
def _interpolate_perspective(self, barycentric, attr0, attr1, attr2, w0, w1, w2):
"""Perspective-correct attribute interpolation"""
w = self._compute_perspective_w(barycentric, w0, w1, w2)
return w * (
attr0 * barycentric[0]/w0 +
attr1 * barycentric[1]/w1 +
attr2 * barycentric[2]/w2
)
def rasterize_triangle(self, v0, v1, v2, framebuffer_width, framebuffer_height,
msaa_samples=1, conservative=False):
"""
Rasterize triangle with modern features:
- Edge function rasterization
- Perspective-correct interpolation
- MSAA support
- Conservative rasterization option
Args:
v0, v1, v2: vertices with (x,y,z,w) coordinates and attributes
msaa_samples: number of MSAA samples (1, 2, 4, or 8)
conservative: use conservative rasterization
"""
fragments = []
# Extract positions and compute W for perspective correction
pos0, pos1, pos2 = v0['position'], v1['position'], v2['position']
w0, w1, w2 = pos0[3], pos1[3], pos2[3]
# Convert to screen space
screen0 = [(pos0[0]/w0 + 1)*0.5*framebuffer_width,
(pos0[1]/w0 + 1)*0.5*framebuffer_height]
screen1 = [(pos1[0]/w1 + 1)*0.5*framebuffer_width,
(pos1[1]/w1 + 1)*0.5*framebuffer_height]
screen2 = [(pos2[0]/w2 + 1)*0.5*framebuffer_width,
(pos2[1]/w2 + 1)*0.5*framebuffer_height]
# Compute bounding box
min_x = max(0, int(min(screen0[0], screen1[0], screen2[0])))
max_x = min(framebuffer_width - 1, int(max(screen0[0], screen1[0], screen2[0])))
min_y = max(0, int(min(screen0[1], screen1[1], screen2[1])))
max_y = min(framebuffer_height - 1, int(max(screen0[1], screen1[1], screen2[1])))
# For conservative rasterization, expand bounding box
if conservative:
min_x -= 1
min_y -= 1
max_x += 1
max_y += 1
# Compute edge functions for triangle edges
def edge01(px, py): return self._compute_edge_function(
screen0[0], screen0[1], screen1[0], screen1[1], px, py)
def edge12(px, py): return self._compute_edge_function(
screen1[0], screen1[1], screen2[0], screen2[1], px, py)
def edge20(px, py): return self._compute_edge_function(
screen2[0], screen2[1], screen0[0], screen0[1], px, py)
# Determine fill rules for edges
is_top_left01 = self._is_top_left_edge(screen0[0], screen0[1],
screen1[0], screen1[1])
is_top_left12 = self._is_top_left_edge(screen1[0], screen1[1],
screen2[0], screen2[1])
is_top_left20 = self._is_top_left_edge(screen2[0], screen2[1],
screen0[0], screen0[1])
# Area of the triangle for barycentric coordinates
area = edge01(screen2[0], screen2[1])
if area <= 0: # Skip back-facing triangles
return []
# MSAA sample positions (for 2x2 grid)
if msaa_samples == 4:
sample_positions = [
(-0.375, -0.375), (0.375, -0.375),
(-0.375, 0.375), (0.375, 0.375)
]
else:
sample_positions = [(0.0, 0.0)]
# Rasterize
for y in range(min_y, max_y + 1):
for x in range(min_x, max_x + 1):
covered_samples = 0
sample_fragments = []
# Test each sample position
for sample_x, sample_y in sample_positions:
px, py = x + sample_x, y + sample_y
# Compute edge values
e01 = edge01(px, py)
e12 = edge12(px, py)
e20 = edge20(px, py)
# Apply fill rules
inside = (
(e01 > 0 or (e01 == 0 and is_top_left01)) and
(e12 > 0 or (e12 == 0 and is_top_left12)) and
(e20 > 0 or (e20 == 0 and is_top_left20))
)
if inside or (conservative and (e01 >= 0 and e12 >= 0 and e20 >= 0)):
covered_samples += 1
# Compute barycentric coordinates
b0 = e12 / area
b1 = e20 / area
b2 = e01 / area
# Interpolate Z perspectively
z = self._interpolate_perspective(
(b0, b1, b2),
pos0[2], pos1[2], pos2[2],
w0, w1, w2
)
# Interpolate attributes
attributes = {}
for attr in v0['attributes'].keys():
attributes[attr] = self._interpolate_perspective(
(b0, b1, b2),
v0['attributes'][attr],
v1['attributes'][attr],
v2['attributes'][attr],
w0, w1, w2
)
sample_fragments.append({
"x": x,
"y": y,
"sample_x": sample_x,
"sample_y": sample_y,
"depth": z,
"attributes": attributes,
"barycentric": (b0, b1, b2)
})
if covered_samples > 0:
fragment = {
"x": x,
"y": y,
"samples": sample_fragments,
"coverage": covered_samples / len(sample_positions)
}
fragments.append(fragment)
return fragments
class HiZBuffer:
"""Hierarchical Z-buffer for early depth testing"""
def __init__(self, width, height):
self.width = width
self.height = height
self.levels = []
# Build mip chain
current_w, current_h = width, height
while current_w > 0 and current_h > 0:
self.levels.append(np.full((current_h, current_w), 1.0))
current_w //= 2
current_h //= 2
def update_region(self, x, y, z):
"""Update Hi-Z pyramid after depth write"""
level = 0
while level < len(self.levels):
level_x, level_y = x >> level, y >> level
if level_x >= self.levels[level].shape[1] or level_y >= self.levels[level].shape[0]:
break
# Update min depth
self.levels[level][level_y, level_x] = min(
self.levels[level][level_y, level_x], z)
level += 1
def test_region(self, min_x, min_y, max_x, max_y, z):
"""Test if region could be visible (not occluded)"""
# Find appropriate mip level
width = max_x - min_x + 1
height = max_y - min_y + 1
level = max(0, int(np.log2(max(width, height))))
if level >= len(self.levels):
return True
# Scale coordinates to mip level
level_min_x = min_x >> level
level_min_y = min_y >> level
level_max_x = max_x >> level
level_max_y = max_y >> level
# Get min depth in region
min_depth = np.inf
for ly in range(level_min_y, level_max_y + 1):
for lx in range(level_min_x, level_max_x + 1):
if ly < self.levels[level].shape[0] and lx < self.levels[level].shape[1]:
min_depth = min(min_depth, self.levels[level][ly, lx])
return z <= min_depth
def process_fragments(self, fragments, fragment_shader_program, chip_id=0,
early_z=True, hierarchical_z=True):
"""
Process fragments using the fragment shader with early-Z and Hi-Z optimizations
Args:
fragments: List of fragments to process
fragment_shader_program: Shader program to execute
chip_id: GPU chip to use
early_z: Enable early-Z optimization
hierarchical_z: Enable hierarchical Z-buffer
"""
processed_fragments = []
# Initialize Hi-Z buffer if needed
hiz = None
if hierarchical_z:
fb_width = max(f["x"] for f in fragments) + 1
fb_height = max(f["y"] for f in fragments) + 1
hiz = self.HiZBuffer(fb_width, fb_height)
# Group fragments into tiles for better cache coherency
TILE_SIZE = 32
tiles = {}
for fragment in fragments:
tile_x = fragment["x"] // TILE_SIZE
tile_y = fragment["y"] // TILE_SIZE
if (tile_x, tile_y) not in tiles:
tiles[(tile_x, tile_y)] = []
tiles[(tile_x, tile_y)].append(fragment)
# Process tiles
for (tile_x, tile_y), tile_fragments in tiles.items():
# Sort fragments by depth for early-Z efficiency
if early_z:
tile_fragments.sort(key=lambda f: f["samples"][0]["depth"])
# Hi-Z test for entire tile
tile_min_x = tile_x * TILE_SIZE
tile_min_y = tile_y * TILE_SIZE
tile_max_x = min(tile_min_x + TILE_SIZE - 1, fb_width - 1)
tile_max_y = min(tile_min_y + TILE_SIZE - 1, fb_height - 1)
if hierarchical_z:
min_depth = min(s["depth"] for f in tile_fragments for s in f["samples"])
if not hiz.test_region(tile_min_x, tile_min_y, tile_max_x, tile_max_y, min_depth):
continue
# Process fragments in tile
for fragment in tile_fragments:
# Early-Z test (per sample)
if early_z:
depth_test_passed = False
for sample in fragment["samples"]:
if self._depth_test(sample["depth"], fragment["x"], fragment["y"]):
depth_test_passed = True
break
if not depth_test_passed:
continue
# Execute fragment shader
processed_samples = []
for sample in fragment["samples"]:
color = self._execute_fragment_shader(sample, fragment_shader_program, chip_id)
processed_sample = {
"sample_x": sample["sample_x"],
"sample_y": sample["sample_y"],
"depth": sample["depth"],
"color": color
}
processed_samples.append(processed_sample)
# Update Hi-Z buffer
if hierarchical_z:
hiz.update_region(fragment["x"], fragment["y"], sample["depth"])
processed_fragment = {
"x": fragment["x"],
"y": fragment["y"],
"samples": processed_samples,
"coverage": fragment["coverage"]
}
processed_fragments.append(processed_fragment)
return processed_fragments
def _execute_fragment_shader(self, fragment, fragment_shader_program, chip_id):
"""
Simulate execution of a fragment shader for a single fragment.
"""
# In a real implementation, this would dispatch the shader instructions
# to an available SM and execute them using the SM's cores.
# For simulation, just return a dummy color based on fragment position
r = (fragment["x"] % 256) / 255.0
g = (fragment["y"] % 256) / 255.0
b = fragment["depth"]
a = 1.0
return (r, g, b, a)
def _depth_test(self, fragment_depth: float, x: int, y: int,
depth_func=lambda a,b: a < b) -> bool:
"""
Test fragment depth against depth buffer
Args:
fragment_depth: Fragment's depth value
x, y: Fragment coordinates
depth_func: Depth comparison function
Returns:
bool: True if fragment passes depth test
"""
depth_buffer_index = y * self.framebuffer_width + x
current_depth = self.depth_buffer[depth_buffer_index]
return depth_func(fragment_depth, current_depth)
def depth_test(self, fragments: List[Dict], depth_buffer_bytes: bytes,
framebuffer_width: int,
depth_func: str = 'LESS',
depth_write: bool = True,
stencil_enabled: bool = False) -> Tuple[List[Dict], bytes]:
"""
Perform depth and optional stencil testing on fragments
Args:
fragments: List of fragments to test
depth_buffer_bytes: Current depth buffer
framebuffer_width: Width of framebuffer
depth_func: Depth comparison function ('LESS', 'LEQUAL', etc)
depth_write: Whether to write passing fragments to depth buffer
stencil_enabled: Whether to perform stencil testing
Returns:
Tuple of (passed fragments, modified depth buffer)
"""
self.framebuffer_width = framebuffer_width
# Set up depth comparison function
depth_funcs = {
'NEVER': lambda a,b: False,
'LESS': lambda a,b: a < b,
'EQUAL': lambda a,b: abs(a - b) < 1e-6,
'LEQUAL': lambda a,b: a <= b,
'GREATER': lambda a,b: a > b,
'NOTEQUAL': lambda a,b: abs(a - b) >= 1e-6,
'GEQUAL': lambda a,b: a >= b,
'ALWAYS': lambda a,b: True
}
depth_compare = depth_funcs[depth_func]
# Unpack depth buffer
self.depth_buffer = []
if depth_buffer_bytes:
for i in range(0, len(depth_buffer_bytes), 4):
depth = struct.unpack("f", bytes(bytearray(depth_buffer_bytes[i:i+4])))[0]
self.depth_buffer.append(depth)
else:
self.depth_buffer = [1.0] * (framebuffer_width * framebuffer_width)
passed_fragments = []
for fragment in fragments:
x, y = fragment["x"], fragment["y"]
passed_samples = []
for sample in fragment["samples"]:
if self._depth_test(sample["depth"], x, y, depth_compare):
passed_samples.append(sample)
# Write depth if enabled
if depth_write:
depth_idx = y * framebuffer_width + x
self.depth_buffer[depth_idx] = sample["depth"]
if passed_samples:
fragment = fragment.copy()
fragment["samples"] = passed_samples
fragment["coverage"] = len(passed_samples) / len(fragment["samples"])
passed_fragments.append(fragment)
# Pack modified depth buffer
modified_depth_buffer = b''.join(
[struct.pack("f", d) for d in self.depth_buffer])
return passed_fragments, modified_depth_buffer
class BlendMode(Enum):
"""Blend modes for color blending"""
ZERO = auto()
ONE = auto()
SRC_COLOR = auto()
ONE_MINUS_SRC_COLOR = auto()
DST_COLOR = auto()
ONE_MINUS_DST_COLOR = auto()
SRC_ALPHA = auto()
ONE_MINUS_SRC_ALPHA = auto()
DST_ALPHA = auto()
ONE_MINUS_DST_ALPHA = auto()
class BlendOp(Enum):
"""Blend operations"""
ADD = auto()
SUBTRACT = auto()
REVERSE_SUBTRACT = auto()
MIN = auto()
MAX = auto()
def _blend_factor(self, mode: BlendMode, src_color, dst_color) -> np.ndarray:
"""Calculate blend factor based on mode"""
if mode == self.BlendMode.ZERO:
return np.zeros(4)
elif mode == self.BlendMode.ONE:
return np.ones(4)
elif mode == self.BlendMode.SRC_COLOR:
return src_color
elif mode == self.BlendMode.ONE_MINUS_SRC_COLOR:
return 1.0 - src_color
elif mode == self.BlendMode.DST_COLOR:
return dst_color
elif mode == self.BlendMode.ONE_MINUS_DST_COLOR:
return 1.0 - dst_color
elif mode == self.BlendMode.SRC_ALPHA:
return np.full(4, src_color[3])
elif mode == self.BlendMode.ONE_MINUS_SRC_ALPHA:
return np.full(4, 1.0 - src_color[3])
elif mode == self.BlendMode.DST_ALPHA:
return np.full(4, dst_color[3])
elif mode == self.BlendMode.ONE_MINUS_DST_ALPHA:
return np.full(4, 1.0 - dst_color[3])
def _blend_operation(self, op: BlendOp, src: np.ndarray, dst: np.ndarray) -> np.ndarray:
"""Apply blend operation"""
if op == self.BlendOp.ADD:
return src + dst
elif op == self.BlendOp.SUBTRACT:
return src - dst
elif op == self.BlendOp.REVERSE_SUBTRACT:
return dst - src
elif op == self.BlendOp.MIN:
return np.minimum(src, dst)
elif op == self.BlendOp.MAX:
return np.maximum(src, dst)
def write_to_framebuffer(self, fragments: List[Dict], color_buffer: bytearray,
framebuffer_width: int,
blend_enable: bool = True,
src_blend: BlendMode = BlendMode.SRC_ALPHA,
dst_blend: BlendMode = BlendMode.ONE_MINUS_SRC_ALPHA,
blend_op: BlendOp = BlendOp.ADD) -> bytearray:
"""
Write fragments to framebuffer with MSAA resolve and blending
Args:
fragments: List of fragments to write
color_buffer: Current framebuffer contents
framebuffer_width: Width of framebuffer
blend_enable: Whether to enable blending
src_blend: Source blend factor
dst_blend: Destination blend factor
blend_op: Blend operation
Returns:
Modified color buffer
"""
for fragment in fragments:
x, y = fragment["x"], fragment["y"]
buffer_index = (y * framebuffer_width + x) * 4
# Read current framebuffer color
dst_color = np.array([
color_buffer[buffer_index] / 255.0,
color_buffer[buffer_index + 1] / 255.0,
color_buffer[buffer_index + 2] / 255.0,
color_buffer[buffer_index + 3] / 255.0
])
# Resolve MSAA samples
if len(fragment["samples"]) > 1:
# Weight colors by coverage
src_color = np.zeros(4)
total_weight = 0.0
for sample in fragment["samples"]:
weight = fragment["coverage"] / len(fragment["samples"])
src_color += np.array(sample["color"]) * weight
total_weight += weight
if total_weight > 0:
src_color /= total_weight
else:
src_color = np.array(fragment["samples"][0]["color"])
# Apply blending if enabled
if blend_enable:
src_factor = self._blend_factor(src_blend, src_color, dst_color)
dst_factor = self._blend_factor(dst_blend, src_color, dst_color)
final_color = self._blend_operation(
blend_op,
src_color * src_factor,
dst_color * dst_factor
)
else:
final_color = src_color
# Clamp and convert to 8-bit
final_color = np.clip(final_color, 0.0, 1.0)
color_buffer[buffer_index] = int(final_color[0] * 255)
color_buffer[buffer_index + 1] = int(final_color[1] * 255)
color_buffer[buffer_index + 2] = int(final_color[2] * 255)
color_buffer[buffer_index + 3] = int(final_color[3] * 255)
return color_buffer
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