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[mtl canvas] Fixed loop implicit matrix

This commit is contained in:
Martin Fouilleul 2023-04-07 10:15:37 +02:00
parent c4e866d9d4
commit d1fab449bc
5 changed files with 519 additions and 123 deletions
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2
build.sh
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@ -55,7 +55,7 @@ fi
if [ $target = 'lib' ] ; then
# compile metal shader
xcrun -sdk macosx metal $shaderFlagParam -c -o $BINDIR/mtl_renderer.air $SRCDIR/mtl_renderer.metal
xcrun -sdk macosx metal $shaderFlagParam -fno-fast-math -c -o $BINDIR/mtl_renderer.air $SRCDIR/mtl_renderer.metal
xcrun -sdk macosx metallib -o $RESDIR/mtl_renderer.metallib $BINDIR/mtl_renderer.air
# compile milepost. We use one compilation unit for all C code, and one compilation

1
examples/polygon/main.c
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@ -151,7 +151,6 @@ int main()
mg_set_color_rgba(0, 0, 1, 1);
mg_stroke();
/*
mg_move_to(x+8, y+8);
mg_line_to(x+33, y+8);

2
src/mtl_renderer.h
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@ -33,6 +33,7 @@ typedef enum {
typedef struct mg_mtl_path_elt
{
int pathIndex;
int localEltIndex;
mg_mtl_seg_kind kind;
vector_float2 p[4];
} mg_mtl_path_elt;
@ -51,6 +52,7 @@ typedef struct mg_mtl_segment
mg_mtl_seg_config config; //TODO pack these
int windingIncrement;
vector_float4 box;
matrix_float3x3 hullMatrix;
matrix_float3x3 implicitMatrix;
int debugID;

68
src/mtl_renderer.m
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@ -88,8 +88,9 @@ typedef struct mg_mtl_encoding_context
int mtlEltCount;
mg_mtl_path_elt* elementBufferData;
int pathIndex;
int localEltIndex;
mg_primitive* primitive;
vec4 pathExtents;
vec4 pathScreenExtents;
} mg_mtl_encoding_context;
@ -121,10 +122,12 @@ void mg_mtl_canvas_encode_element(mg_mtl_encoding_context* context, mg_path_elt_
break;
}
mtlElt->localEltIndex = context->localEltIndex;
for(int i=0; i<count; i++)
{
mg_update_path_extents(&context->pathExtents, p[i]);
vec2 screenP = mg_mat2x3_mul(context->primitive->attributes.transform, p[i]);
mg_update_path_extents(&context->pathScreenExtents, screenP);
mtlElt->p[i] = (vector_float2){screenP.x, screenP.y};
}
}
@ -155,6 +158,19 @@ void mg_mtl_render_stroke_quadratic(mg_mtl_encoding_context* context, vec2* p)
f32 width = context->primitive->attributes.width;
f32 tolerance = minimum(context->primitive->attributes.tolerance, 0.5 * width);
//NOTE: check for degenerate line case
const f32 equalEps = 1e-3;
if(vec2_close(p[0], p[1], equalEps))
{
mg_mtl_render_stroke_line(context, p+1);
return;
}
else if(vec2_close(p[1], p[2], equalEps))
{
mg_mtl_render_stroke_line(context, p);
return;
}
vec2 leftHull[3];
vec2 rightHull[3];
@ -233,6 +249,30 @@ void mg_mtl_render_stroke_cubic(mg_mtl_encoding_context* context, vec2* p)
f32 width = context->primitive->attributes.width;
f32 tolerance = minimum(context->primitive->attributes.tolerance, 0.5 * width);
//NOTE: check degenerate line cases
f32 equalEps = 1e-3;
if( (vec2_close(p[0], p[1], equalEps) && vec2_close(p[2], p[3], equalEps))
||(vec2_close(p[0], p[1], equalEps) && vec2_close(p[1], p[2], equalEps))
||(vec2_close(p[1], p[2], equalEps) && vec2_close(p[2], p[3], equalEps)))
{
vec2 line[2] = {p[0], p[3]};
mg_mtl_render_stroke_line(context, line);
return;
}
else if(vec2_close(p[0], p[1], equalEps) && vec2_close(p[1], p[3], equalEps))
{
vec2 line[2] = {p[0], vec2_add(vec2_mul(5./9, p[0]), vec2_mul(4./9, p[2]))};
mg_mtl_render_stroke_line(context, line);
return;
}
else if(vec2_close(p[0], p[2], equalEps) && vec2_close(p[2], p[3], equalEps))
{
vec2 line[2] = {p[0], vec2_add(vec2_mul(5./9, p[0]), vec2_mul(4./9, p[1]))};
mg_mtl_render_stroke_line(context, line);
return;
}
vec2 leftHull[4];
vec2 rightHull[4];
@ -373,10 +413,6 @@ void mg_mtl_stroke_cap(mg_mtl_encoding_context* context,
vec2 p0,
vec2 direction)
{
//////////////////////////////////////////////////////////
//TODO: fix orientation here!
//////////////////////////////////////////////////////////
mg_attributes* attributes = &context->primitive->attributes;
//NOTE(martin): compute the tangent and normal vectors (multiplied by half width) at the cap point
@ -525,7 +561,6 @@ u32 mg_mtl_render_stroke_subpath(mg_mtl_encoding_context* context,
{
//NOTE(martin): add a closing joint if the path is closed
mg_mtl_stroke_joint(context, endPoint, endTangent, firstTangent);
printf("closing joint for shape %i\n", context->pathIndex);
}
}
else if(attributes->cap == MG_CAP_SQUARE)
@ -592,25 +627,30 @@ void mg_mtl_canvas_render(mg_canvas_backend* interface,
if(primitive->path.count)
{
context.primitive = primitive;
context.pathIndex = primitiveIndex;
context.pathExtents = (vec4){FLT_MAX, FLT_MAX, -FLT_MAX, -FLT_MAX};
context.pathIndex = pathCount;
context.pathScreenExtents = (vec4){FLT_MAX, FLT_MAX, -FLT_MAX, -FLT_MAX};
if(primitive->cmd == MG_CMD_STROKE)
{
mg_mtl_render_stroke(&context, pathElements + primitive->path.startIndex, &primitive->path);
continue;
// mg_mtl_render_stroke(&context, pathElements + primitive->path.startIndex, &primitive->path);
}
else
{
int segCount = 0;
for(int eltIndex = 0;
(eltIndex < primitive->path.count) && (primitive->path.startIndex + eltIndex < eltCount);
eltIndex++)
{
context.localEltIndex = segCount;
mg_path_elt* elt = &pathElements[primitive->path.startIndex + eltIndex];
if(elt->type != MG_PATH_MOVE)
{
vec2 p[4] = {currentPos, elt->p[0], elt->p[1], elt->p[2]};
mg_mtl_canvas_encode_element(&context, elt->type, p);
segCount++;
}
switch(elt->type)
{
@ -637,10 +677,10 @@ void mg_mtl_canvas_render(mg_canvas_backend* interface,
pathCount++;
path->cmd = (mg_mtl_cmd)primitive->cmd;
path->box = (vector_float4){maximum(primitive->attributes.clip.x, context.pathExtents.x),
maximum(primitive->attributes.clip.y, context.pathExtents.y),
minimum(primitive->attributes.clip.x + primitive->attributes.clip.w, context.pathExtents.z),
minimum(primitive->attributes.clip.y + primitive->attributes.clip.h, context.pathExtents.w)};
path->box = (vector_float4){maximum(primitive->attributes.clip.x, context.pathScreenExtents.x),
maximum(primitive->attributes.clip.y, context.pathScreenExtents.y),
minimum(primitive->attributes.clip.x + primitive->attributes.clip.w, context.pathScreenExtents.z),
minimum(primitive->attributes.clip.y + primitive->attributes.clip.h, context.pathScreenExtents.w)};
path->color = (vector_float4){primitive->attributes.color.r,
primitive->attributes.color.g,

573
src/mtl_renderer.metal
View File

@ -65,8 +65,10 @@ void mtl_log(mtl_log_context context, const thread char* msg)
}
}
int mtl_itoa(int bufSize, thread char* buffer, thread char** start, int64_t value)
int mtl_itoa_right_aligned(int bufSize, thread char* buffer, int64_t value, bool zeroPad)
{
// convert value to a null-terminated string at end of buffer and returns the size
// (excluding the final null).
bool minus = false;
if(value < 0)
{
@ -75,12 +77,23 @@ int mtl_itoa(int bufSize, thread char* buffer, thread char** start, int64_t valu
}
buffer[bufSize-1] = '\0';
int index = bufSize-2;
int stop = minus ? 1 : 0;
do
{
buffer[index] = '0' + (value % 10);
index--;
value /= 10;
} while(value != 0 && index >= 1);
} while(value != 0 && index >= stop);
if(zeroPad)
{
while(index >= stop)
{
buffer[index] = '0';
index--;
}
}
if(minus)
{
@ -88,62 +101,110 @@ int mtl_itoa(int bufSize, thread char* buffer, thread char** start, int64_t valu
index--;
}
*start = buffer+index+1;
return(bufSize - (index+1) - 1);
int count = bufSize - (index+1);
return(count - 1);
}
int mtl_itoa(int bufSize, thread char* buffer, int64_t value)
{
int count = mtl_itoa_right_aligned(bufSize, buffer, value, false);
int start = bufSize - (count+1);
for(int i=0; i<count+1; i++)
{
buffer[i] = buffer[start+i];
}
return(count);
}
void mtl_log_i32(mtl_log_context context, int value)
{
char buffer[12];
thread char* start = 0;
mtl_itoa(12, buffer, &start, value);
mtl_log(context, start);
mtl_itoa(12, buffer, value);
mtl_log(context, buffer);
}
void mtl_log_f32(mtl_log_context context, float value)
{
int64_t integral = (int64_t)value;
int64_t decimal = (int64_t)((value - (float)integral)*1e9);
bool minus = false;
if(value < 0)
{
minus = true;
value *= -1;
}
while(decimal && (decimal % 10 == 0))
{
decimal /= 10;
}
while(decimal > 999999)
{
decimal /= 10;
}
if(decimal < 0)
{
decimal *= -1;
}
int64_t integral = (int64_t)value;
int64_t decimal = (int64_t)((value - (float)integral)*1e6);
const int bufSize = 64;
char buffer[bufSize];
thread char* start = 0;
int integralSize = mtl_itoa(bufSize, buffer, &start, integral);
for(int i=0; i<integralSize; i++)
int index = 0;
if(minus)
{
buffer[i] = start[i];
buffer[index] = '-';
index++;
}
index += mtl_itoa(bufSize-index, buffer+index, integral);
if(index < bufSize && decimal)
{
buffer[index] = '.';
index++;
int width = 6;
while(decimal % 10 == 0 && width > 0)
{
decimal /= 10;
width--;
}
int decimalSize = 0;
if(integralSize < bufSize && decimal)
{
buffer[integralSize] = '.';
integralSize++;
decimalSize = mtl_itoa(bufSize - integralSize - 1, buffer, &start, decimal);
for(int i=0; i<decimalSize; i++)
{
buffer[integralSize+i] = start[i];
int decSize = min(bufSize-index, width+1);
mtl_itoa_right_aligned(decSize, buffer+index, decimal, true);
}
}
buffer[integralSize+decimalSize] = '\0';
buffer[bufSize-1] = '\0';
mtl_log(context, buffer);
}
void mtl_log_point(mtl_log_context context, float2 p)
{
mtl_log(context, "(");
mtl_log_f32(context, p.x);
mtl_log(context, ", ");
mtl_log_f32(context, p.y);
mtl_log(context, ")");
}
void log_line(thread float2* p, mtl_log_context logCtx)
{
mtl_log(logCtx, "(");
mtl_log_f32(logCtx, p[0].x);
mtl_log(logCtx, ", ");
mtl_log_f32(logCtx, p[0].y);
mtl_log(logCtx, ") (");
mtl_log_f32(logCtx, p[1].x);
mtl_log(logCtx, ", ");
mtl_log_f32(logCtx, p[1].y);
mtl_log(logCtx, ")\n");
}
void log_quadratic_bezier(thread float2* p, mtl_log_context logCtx)
{
mtl_log(logCtx, "(");
mtl_log_f32(logCtx, p[0].x);
mtl_log(logCtx, ", ");
mtl_log_f32(logCtx, p[0].y);
mtl_log(logCtx, ") (");
mtl_log_f32(logCtx, p[1].x);
mtl_log(logCtx, ", ");
mtl_log_f32(logCtx, p[1].y);
mtl_log(logCtx, ") (");
mtl_log_f32(logCtx, p[2].x);
mtl_log(logCtx, ", ");
mtl_log_f32(logCtx, p[2].y);
mtl_log(logCtx, ")\n");
}
void log_cubic_bezier(thread float2* p, mtl_log_context logCtx)
{
mtl_log(logCtx, "(");
@ -258,8 +319,16 @@ int mtl_side_of_segment(float2 p, const device mg_mtl_segment* seg, mtl_log_cont
case MG_MTL_CUBIC:
{
float3 ph = {p.x, p.y, 1};
float3 hullCoords = seg->hullMatrix * ph;
if(all(hullCoords > 0))
{
float3 klm = seg->implicitMatrix * ph;
side = (klm.x*klm.x*klm.x - klm.y*klm.z < 0)? -1 : 1;
}
else
{
side = (seg->config == MG_MTL_BL || seg->config == MG_MTL_TL) ? -1 : 1;
}
} break;
}
}
@ -391,17 +460,20 @@ device mg_mtl_segment* mtl_segment_push(thread mtl_segment_setup_context* contex
break;
case MG_MTL_CUBIC:
s = p[0];
if(any(p[1] != p[0]))
{
c = p[1];
}
else
s = p[0];
float sqrNorm0 = length_squared(p[1]-p[0]);
float sqrNorm1 = length_squared(p[3]-p[2]);
if(sqrNorm0 < sqrNorm1)
{
c = p[2];
}
else
{
c = p[1];
}
e = p[3];
break;
} break;
}
int segIndex = atomic_fetch_add_explicit(context->segmentCount, 1, memory_order_relaxed);
@ -513,6 +585,16 @@ int mtl_quadratic_monotonize(float2 p[3], float splits[4])
return(count);
}
matrix_float3x3 mtl_barycentric_matrix(float2 v0, float2 v1, float2 v2)
{
float det = v0.x*(v1.y-v2.y) + v1.x*(v2.y-v0.y) + v2.x*(v0.y - v1.y);
matrix_float3x3 B = {{v1.y - v2.y, v2.y-v0.y, v0.y-v1.y},
{v2.x - v1.x, v0.x-v2.x, v1.x-v0.x},
{v1.x*v2.y-v2.x*v1.y, v2.x*v0.y-v0.x*v2.y, v0.x*v1.y-v1.x*v0.y}};
B *= (1/det);
return(B);
}
void mtl_quadratic_emit(thread mtl_segment_setup_context* context,
thread float2* p)
{
@ -552,25 +634,86 @@ void mtl_quadratic_setup(thread mtl_segment_setup_context* context, thread float
}
}
int mtl_quadratic_roots(float a, float b, float c, thread float* r)
/*
diff_of_products() computes a*b-c*d with a maximum error <= 1.5 ulp
Claude-Pierre Jeannerod, Nicolas Louvet, and Jean-Michel Muller,
"Further Analysis of Kahan's Algorithm for the Accurate Computation
of 2x2 Determinants". Mathematics of Computation, Vol. 82, No. 284,
Oct. 2013, pp. 2245-2264
*/
float diff_of_products (float a, float b, float c, float d)
{
//TODO: replace by something more numerically stable
int count = 0;
float det = square(b) - 4*a*c;
if(det > 0)
{
count = 2;
r[0] = (-b - sqrt(det))/(2*a);
r[1] = (-b + sqrt(det))/(2*a);
float w = d * c;
float e = fma(-d, c, w);
float f = fma(a, b, -w);
return(f + e);
}
else if(det == 0)
int mtl_quadratic_roots_with_det(float a, float b, float c, float det, thread float* r, mtl_log_context log = {.enabled = false})
{
int count = 0;
if(a == 0)
{
if(b)
{
count = 1;
r[0] = -b/(2*a);
r[0] = -c/b;
}
}
else
{
b /= 2.0;
if(det >= 0)
{
count = (det == 0) ? 1 : 2;
if(b > 0)
{
float q = b + sqrt(det);
r[0] = -c/q;
r[1] = -q/a;
}
else if(b < 0)
{
float q = -b + sqrt(det);
r[0] = q/a;
r[1] = c/q;
}
else
{
float q = sqrt(-a*c);
if(fabs(a) >= fabs(c))
{
r[0] = q/a;
r[1] = -q/a;
}
else
{
r[0] = -c/q;
r[1] = c/q;
}
}
}
}
if(count>1 && r[0] > r[1])
{
float tmp = r[0];
r[0] = r[1];
r[1] = tmp;
}
return(count);
}
int mtl_quadratic_roots(float a, float b, float c, thread float* r, mtl_log_context log = {.enabled = false})
{
//float det = diff_of_products(b, b, a, c);
float det = square(b)/4. - a*c;
return(mtl_quadratic_roots_with_det(a, b, c, det, r, log));
}
void mtl_cubic_slice(float2 p[4], float s0, float s1, float2 sp[4])
{
float sr = (s1 - s0)/(1-s0);
@ -597,7 +740,7 @@ void mtl_cubic_slice(float2 p[4], float s0, float s1, float2 sp[4])
sp[3] = float2(qx.w, qy.w);
}
int mtl_cubic_monotonize(float2 p[4], float splits[8])
int mtl_cubic_monotonize(float2 p[4], float splits[8], mtl_log_context log)
{
//NOTE(martin): first convert the control points to power basis
float2 c[4];
@ -612,10 +755,31 @@ int mtl_cubic_monotonize(float2 p[4], float splits[8])
rootCount += mtl_quadratic_roots(3*c[3].y, 2*c[2].y, c[1].y, roots+rootCount);
//NOTE: compute inflection points
rootCount += mtl_quadratic_roots(6*(c[2].x*c[3].y-c[3].x*c[2].y),
6*(c[1].x*c[3].y-c[1].y*c[3].x),
2*(c[1].x*c[2].y-c[1].y*c[2].x),
roots + rootCount);
rootCount += mtl_quadratic_roots(3*(c[2].x*c[3].y - c[3].x*c[2].y),
3*(c[1].x*c[3].y - c[1].y*c[3].x),
(c[1].x*c[2].y - c[1].y*c[2].x),
roots + rootCount,
log);
/*
mtl_log(log, "bezier basis: ");
log_cubic_bezier(p, log);
mtl_log(log, "power basis: ");
log_cubic_bezier(c, log);
mtl_log(log, "inflection equation: ");
mtl_log_f32(log, 3*(c[2].x*c[3].y-c[3].x*c[2].y));
mtl_log(log, ", ");
mtl_log_f32(log, 3*(c[1].x*c[3].y-c[1].y*c[3].x));
mtl_log(log, ", ");
mtl_log_f32(log, (c[1].x*c[2].y-c[1].y*c[2].x));
mtl_log(log, "\n");
mtl_log(log, "inflection split count: ");
mtl_log_i32(log, rootCount-tmp);
mtl_log(log, "\n");
*/
//NOTE: sort roots
for(int i=1; i<rootCount; i++)
@ -636,6 +800,11 @@ int mtl_cubic_monotonize(float2 p[4], float splits[8])
splitCount++;
for(int i=0; i<rootCount; i++)
{
/*
mtl_log(log, "root: ");
mtl_log_f32(log, roots[i]);
mtl_log(log, "\n");
*/
if(roots[i] > 0 && roots[i] < 1)
{
splits[splitCount] = roots[i];
@ -687,9 +856,9 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
c2 = 3*p0 - 6*p1 + 3*p2
c3 = -p0 + 3*p1 - 3*p2 + p3
*/
float2 c1 = 3.0*p[1] - 3.0*p[0];
float2 c2 = 3.0*p[0] + 3.0*p[2] - 6.0*p[1];
float2 c3 = 3.0*p[1] - 3.0*p[2] + p[3] - p[0];
float2 c1 = 3.0*(p[1] - p[0]);
float2 c2 = 3.0*(p[0] + p[2] - 2*p[1]);
float2 c3 = 3.0*(p[1] - p[2]) + p[3] - p[0];
/*NOTE(martin):
now, compute determinants d0, d1, d2, d3, which gives the coefficients of the
@ -706,32 +875,65 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
In our case, the pi.w equal 1 (no point at infinity), so _in_the_power_basis_, w1 = w2 = w3 = 0 and w0 = 1
(which also means d0 = 0)
*/
float d1 = c3.y*c2.x - c3.x*c2.y;
float d2 = c3.x*c1.y - c3.y*c1.x;
float d3 = c2.y*c1.x - c2.x*c1.y;
//WARN: there seems to be a mismatch between the signs of the d_i and the orientation test in the Loop-Blinn paper?
// flipping the sign of the d_i doesn't change the roots (and the implicit matrix), but it does change the orientation.
// Keeping the signs of the paper puts the interior on the left of parametric travel, unlike what's stated in the paper.
// this may very well be an error on my part that's cancelled by flipping the signs of the d_i though!
*/
/*
mtl_log(log, "bezier basis: ");
log_cubic_bezier(p, log);
float2 c[4] = {p[0], c1, c2, c3};
mtl_log(log, "power basis: ");
log_cubic_bezier(c, log);
*/
float d1 = -(c3.y*c2.x - c3.x*c2.y);
float d2 = -(c3.x*c1.y - c3.y*c1.x);
float d3 = -(c2.y*c1.x - c2.x*c1.y);
// mtl_log(log, "d1 = ");
/* mtl_log_f32(log, d1);
mtl_log(log, ", d2 = ");
mtl_log_f32(log, d2);
mtl_log(log, ", d3 = ");
mtl_log_f32(log, d3);
mtl_log(log, "\n");
*/
//NOTE(martin): compute the second factor of the discriminant discr(I) = d1^2*(3*d2^2 - 4*d3*d1)
float discrFactor2 = 3.0*square(d2) - 4.0*d3*d1;
//NOTE(martin): each following case gives the number of roots, hence the category of the parametric curve
if(fabs(d1) < 0.1 && fabs(d2) < 0.1 && d3 != 0)
if(fabs(d1) < 1e-6 && fabs(d2) < 1e-6 && fabs(d3) > 1e-6)
{
//NOTE(martin): quadratic degenerate case
//NOTE(martin): compute quadratic curve control point, which is at p0 + 1.5*(p1-p0) = 1.5*p1 - 0.5*p0
result.kind = MTL_CUBIC_DEGENERATE_QUADRATIC;
result.quadPoint = float2(1.5*p[1].x - 0.5*p[0].x, 1.5*p[1].y - 0.5*p[0].y);
}
else if( (discrFactor2 > 0 && d1 != 0)
||(discrFactor2 == 0 && d1 != 0))
else if( (discrFactor2 > 0 && fabs(d1) > 1e-6)
||(discrFactor2 == 0 && fabs(d1) > 1e-6))
{
//NOTE(martin): serpentine curve or cusp with inflection at infinity
// (these two cases are handled the same way).
//NOTE(martin): compute the solutions (tl, sl), (tm, sm), and (tn, sn) of the inflection point equation
float tl = d2 + sqrt(discrFactor2/3);
float tmtl[2];
mtl_quadratic_roots_with_det(1, -2*d2, (4./3.*d1*d3), (1./3.)*discrFactor2, tmtl);
float tm = tmtl[0];
float sm = 2*d1;
float tl = tmtl[1];
float sl = 2*d1;
float tm = d2 - sqrt(discrFactor2/3);
float sm = sl;
float invNorm = 1/sqrt(square(tm) + square(sm));
tm *= invNorm;
sm *= invNorm;
invNorm = 1/sqrt(square(tl) + square(sl));
tl *= invNorm;
sl *= invNorm;
/*NOTE(martin):
the power basis coefficients of points k,l,m,n are collected into the rows of the 4x4 matrix F:
@ -749,31 +951,61 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
{1, 0, 0, 0}};
//NOTE: if necessary, flip sign of k and l to ensure the interior is west from the curve
float flip = (d1 < 0)^(p[3].y < p[0].y) ? -1 : 1;
float flip = (d1 < 0)? -1 : 1;
if(p[3].y > p[0].y)
{
flip *= -1;
}
F[0] *= flip;
F[1] *= flip;
}
else if(discrFactor2 < 0 && d1 != 0)
else if(discrFactor2 < 0 && fabs(d1) > 1e-6)
{
//NOTE(martin): loop curve
float td = d2 + sqrt(-discrFactor2);
float tetd[2];
mtl_quadratic_roots_with_det(1, -2*d2, 4*(square(d2)-d1*d3), -discrFactor2, tetd, log);
float td = tetd[1];
float sd = 2*d1;
float te = d2 - sqrt(-discrFactor2);
float se = sd;
float te = tetd[0];
float se = 2*d1;
float invNorm = 1/sqrt(square(td) + square(sd));
td *= invNorm;
sd *= invNorm;
invNorm = 1/sqrt(square(te) + square(se));
te *= invNorm;
se *= invNorm;
//NOTE(martin): if one of the parameters (td/sd) or (te/se) is in the interval [0,1], the double point
// is inside the control points convex hull and would cause a shading anomaly. If this is
// the case, subdivide the curve at that point
//TODO: study edge case where td/sd ~ 1 or 0 (which causes an infinite recursion in split and fill).
// quick fix for now is adding a little slop in the check...
//*
mtl_log(log, "td = ");
mtl_log_f32(log, td);
mtl_log(log, ", sd = ");
mtl_log_f32(log, sd);
mtl_log(log, ", te = ");
mtl_log_f32(log, te);
mtl_log(log, ", se = ");
mtl_log_f32(log, td);
mtl_log(log, ", td/sd = ");
mtl_log_f32(log, td/sd);
mtl_log(log, ", te/se = ");
mtl_log_f32(log, te/se);
mtl_log(log, "\n");
//*/
//TODO: investigate better margins here. The problem is that if we have a double point around 0 or 1,
// splitting the curve might also produce a root in [0, 1] due to numerical errors.
if(sd != 0 && td/sd < 0.99 && td/sd > 0.01)
{
result.kind = MTL_CUBIC_LOOP_SPLIT;
result.split = td/sd;
}
if(se != 0 && te/se < 0.99 && te/se > 0.01)
else if(se != 0 && te/se < 0.99 && te/se > 0.01)
{
result.kind = MTL_CUBIC_LOOP_SPLIT;
result.split = te/se;
@ -796,21 +1028,43 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
{1, 0, 0, 0}};
//NOTE: if necessary, flip sign of k and l to ensure the interior is west from the curve
float H0 = 36*(d3*d1-square(d2));
float H1 = 36*(d3*d1-square(d2) + d1*d2 - square(d1));
float H0 = d3*d1-square(d2);
float H1 = d3*d1-square(d2) + d1*d2 - square(d1);
float H = (abs(H0) > abs(H1)) ? H0 : H1;
float flip = (H*d1 > 0)^(p[3].y < p[0].y) ? -1 : 1;
float flip = (H*d1 > 0) ? -1 : 1;
/*
mtl_log(log, "H0 = ");
mtl_log_f32(log, H0);
mtl_log(log, ", H1 = ");
mtl_log_f32(log, H1);
mtl_log(log, ", flip = ");
mtl_log_f32(log, flip);
mtl_log(log, "\n");
*/
if(p[3].y > p[0].y)
{
/* mtl_log(log, "fixed flip = ");
mtl_log_f32(log, flip);
mtl_log(log, "\n");
*/
flip *= -1;
}
F[0] *= flip;
F[1] *= flip;
}
}
else if(d1 == 0 && d2 != 0)
else if(d2 != 0)
{
//NOTE(martin): cusp with cusp at infinity
float tl = d3;
float sl = 3*d2;
float invNorm = 1/sqrt(square(tl)+square(sl));
tl *= invNorm;
sl *= invNorm;
/*NOTE(martin):
the power basis coefficients of points k,l,m,n are collected into the rows of the 4x4 matrix F:
@ -831,16 +1085,11 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
F[0] *= flip;
F[1] *= flip;
}
else if(d1 == 0 && d2 == 0 && d3 == 0)
else
{
//NOTE(martin): line or point degenerate case
result.kind = MTL_CUBIC_DEGENERATE_LINE;
}
else
{
//TODO(martin): handle error ? put some epsilon slack on the conditions ?
result.kind = MTL_CUBIC_ERROR;
}
/*
F is then multiplied by M3^(-1) on the left which yelds the bezier coefficients k, l, m, n
@ -861,6 +1110,44 @@ mtl_cubic_info mtl_cubic_classify(thread float2* p, mtl_log_context log = {.enab
return(result);
}
matrix_float3x3 mtl_hull_matrix(float2 p0, float2 p1, float2 p2, float2 p3, mtl_log_context log)
{
/*NOTE: check intersection of lines (p1-p0) and (p3-p2)
P = p0 + u(p1-p0)
P = p2 + w(p3-p2)
control points are inside a right triangle so we should always find an intersection
*/
float2 pm;
float det = (p1.x - p0.x)*(p3.y - p2.y) - (p1.y - p0.y)*(p3.x - p2.x);
float sqrNorm0 = length_squared(p1-p0);
float sqrNorm1 = length_squared(p2-p3);
if(fabs(det) < 1e-3 || sqrNorm0 < 0.1 || sqrNorm1 < 0.1)
{
float sqrNorm0 = length_squared(p1-p0);
float sqrNorm1 = length_squared(p2-p3);
if(sqrNorm0 < sqrNorm1)
{
pm = p2;
}
else
{
pm = p1;
}
}
else
{
float u = ((p0.x - p2.x)*(p2.y - p3.y) - (p0.y - p2.y)*(p2.x - p3.x))/det;
pm = p0 + u*(p1-p0);
}
matrix_float3x3 m = mtl_barycentric_matrix(p0, p3, pm);
return(m);
}
void mtl_cubic_emit(thread mtl_segment_setup_context* context, float2 p[4], mtl_cubic_info info)
{
device mg_mtl_segment* seg = mtl_segment_push(context, p, MG_MTL_CUBIC);
@ -870,7 +1157,10 @@ void mtl_cubic_emit(thread mtl_segment_setup_context* context, float2 p[4], mtl_
float2 v2;
matrix_float3x3 K;
if(any(p[0] != p[1]))
float sqrNorm0 = length_squared(p[1]-p[0]);
float sqrNorm1 = length_squared(p[2]-p[3]);
if(sqrNorm0 >= sqrNorm1)
{
v2 = p[1];
K = {info.K[0].xyz, info.K[3].xyz, info.K[1].xyz};
@ -880,31 +1170,42 @@ void mtl_cubic_emit(thread mtl_segment_setup_context* context, float2 p[4], mtl_
v2 = p[2];
K = {info.K[0].xyz, info.K[3].xyz, info.K[2].xyz};
}
//NOTE: compute barycentric matrix
float det = v0.x*(v1.y-v2.y) + v1.x*(v2.y-v0.y) + v2.x*(v0.y - v1.y);
matrix_float3x3 B = {{v1.y - v2.y, v2.y-v0.y, v0.y-v1.y},
{v2.x - v1.x, v0.x-v2.x, v1.x-v0.x},
{v1.x*v2.y-v2.x*v1.y, v2.x*v0.y-v0.x*v2.y, v0.x*v1.y-v1.x*v0.y}};
B *= (1/det);
//NOTE: set implicit matrix and bin segment
//NOTE: set matrices and bin segment
matrix_float3x3 B = mtl_barycentric_matrix(v0, v1, v2);
seg->implicitMatrix = K*B;
seg->hullMatrix = mtl_hull_matrix(p[0], p[1], p[2], p[3], context->log);
mtl_segment_bin_to_tiles(context, seg);
}
void mtl_cubic_setup(thread mtl_segment_setup_context* context, float2 p[4])
{
float splits[8];
int splitCount = mtl_cubic_monotonize(p, splits);
int splitCount = mtl_cubic_monotonize(p, splits, context->log);
mtl_log(context->log, "curve = ");
log_cubic_bezier(p, context->log);
mtl_log(context->log, "split count = ");
mtl_log_i32(context->log, splitCount-1);
mtl_log(context->log, "\n");
//NOTE: produce bézier curve for each consecutive pair of roots
for(int sliceIndex=0; sliceIndex<splitCount-1; sliceIndex++)
{
/////////////////////////////////////DEBUG
/* if(sliceIndex != 0)
{
continue;
}
*/
float2 sp[4];
mtl_cubic_slice(p, splits[sliceIndex], splits[sliceIndex+1], sp);
mtl_log(context->log, "slice = ");
log_cubic_bezier(sp, context->log);
mtl_cubic_info curve = mtl_cubic_classify(sp, context->log);
switch(curve.kind)
{
@ -926,6 +1227,10 @@ void mtl_cubic_setup(thread mtl_segment_setup_context* context, float2 p[4])
case MTL_CUBIC_LOOP_SPLIT:
{
mtl_log(context->log, "loop split: \n");
mtl_log_f32(context->log, curve.split);
mtl_log(context->log, "\n");
//NOTE: split and reclassify, check that we have a valid loop and emit
float2 ssp[8];
mtl_cubic_slice(sp, 0, curve.split, ssp);
@ -933,18 +1238,35 @@ void mtl_cubic_setup(thread mtl_segment_setup_context* context, float2 p[4])
for(int i=0; i<2; i++)
{
curve = mtl_cubic_classify(ssp + 4*i);
mtl_cubic_info splitCurve = mtl_cubic_classify(ssp + 4*i, context->log);
if(curve.kind != MTL_CUBIC_LOOP_OK)
mtl_log(context->log, "loop slice \n");
mtl_log_i32(context->log, i);
mtl_log(context->log, ": ");
log_cubic_bezier(ssp+i*4, context->log);
mtl_log_i32(context->log, splitCurve.kind);
mtl_log(context->log, "\n");
////////////////////////////////////////////////////////////////////////////////////
//TODO: here the result of mtl_cubic_classify seems to be changed if we print something
// inside it...
// Anyway, we shouldn't reclassify split curves, just find the new hull matrix?
////////////////////////////////////////////////////////////////////////////////////
CONTINUE_HERE;
if(splitCurve.kind == MTL_CUBIC_LOOP_SPLIT)
{
mtl_log(context->log, "loop split left error\n");
mtl_log(context->log, "loop split error (");
mtl_log_f32(context->log, splitCurve.split);
mtl_log(context->log, ") ****************************************\n");
}
else
{
mtl_cubic_emit(context, ssp + 4*i, curve);
mtl_cubic_emit(context, ssp + 4*i, splitCurve);
}
}
}
} break;
case MTL_CUBIC_LOOP_OK:
@ -974,6 +1296,21 @@ kernel void mtl_segment_setup(constant int* elementCount [[buffer(0)]],
{
const device mg_mtl_path_elt* elt = &elementBuffer[eltIndex];
//28
// 125
// 112
if(elt->pathIndex != 124)
{
return;
}
if(elt->localEltIndex != 4)// && elt->localEltIndex != 3)
{
return;
}
const device mg_mtl_path_queue* pathQueue = &pathQueueBuffer[elt->pathIndex];
device mg_mtl_tile_queue* tileQueues = &tileQueueBuffer[pathQueue->tileQueues];
@ -987,19 +1324,27 @@ kernel void mtl_segment_setup(constant int* elementCount [[buffer(0)]],
.tileSize = tileSize[0],
.log.buffer = logBuffer,
.log.offset = logOffsetBuffer,
.log.enabled = (eltIndex == 1)};
.log.enabled = true};
switch(elt->kind)
{
case MG_MTL_LINE:
{
float2 p[2] = {elt->p[0]*scale[0], elt->p[1]*scale[0]};
mtl_log(setupCtx.log, "line: ");
log_line(p, setupCtx.log);
mtl_line_setup(&setupCtx, p);
} break;
case MG_MTL_QUADRATIC:
{
float2 p[3] = {elt->p[0]*scale[0], elt->p[1]*scale[0], elt->p[2]*scale[0]};
mtl_log(setupCtx.log, "quadratic: ");
log_quadratic_bezier(p, setupCtx.log);
mtl_quadratic_setup(&setupCtx, p);
} break;
@ -1172,9 +1517,17 @@ kernel void mtl_raster(const device int* screenTilesBuffer [[buffer(0)]],
pathIndex = op->index;
winding = op->windingOffset;
if(op->next != -1)
{
color = float4(0, 1, 0, 1);
}
}
else if(op->kind == MG_MTL_OP_SEGMENT)
{
// outTexture.write(float4(1, 0, 0, 1), uint2(pixelCoord));
// return;
const device mg_mtl_segment* seg = &segmentBuffer[op->index];
if( (pixelCoord.y > seg->box.y)
@ -1186,6 +1539,8 @@ kernel void mtl_raster(const device int* screenTilesBuffer [[buffer(0)]],
if(op->crossRight)
{
color = float4(0, 1, 1, 1);
if( (seg->config == MG_MTL_BR || seg->config == MG_MTL_TL)
&&(pixelCoord.y > seg->box.w))
{