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u02: Implement barycentric coordinates

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This commit is contained in:
Simon Bruder 2023-05-07 16:25:48 +02:00
parent 2fd207f5f4
commit 04527ef711
3 changed files with 83 additions and 0 deletions
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6
u02/include/util.h
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@ -30,3 +30,9 @@ std::pair<int, int> transform_inv(Transformation transformation, int x, int y);
// to make the given endpoints of a line conform
// to the standard case for rasterization.
Transformation transformation_to_standard_case(int x0, int y0, int x1, int y1);
// Returns the barycentric coordinates of the point given by (xp, yp)
// in the triangle given by the three points (x0, y0), (x1, y1), (x2, y2).
std::tuple<float, float, float> barycentric_coordinates(int x0, int y0, int x1,
int y1, int x2, int y2,
int xp, int yp);

57
u02/src/tests.cpp
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@ -4,6 +4,7 @@
#include <catch2/generators/catch_generators.hpp>
#include <catch2/generators/catch_generators_adapters.hpp>
#include <catch2/generators/catch_generators_random.hpp>
#include <catch2/matchers/catch_matchers_floating_point.hpp>
#include "bresenham_circle_tool.h"
#include "bresenham_line_tool.h"
@ -14,6 +15,8 @@
#include "recursive_fill_tool.h"
#include "util.h"
using Catch::Matchers::WithinRel;
TEST_CASE("Transform Mirror") {
// elementary operations
REQUIRE(transform(TRANSFORM_MIRROR_X, 10, 20) == std::make_pair(10, -20));
@ -370,3 +373,57 @@ TEST_CASE("Bresenham circle (prop: √(x²+y²)-r<ε)") {
}
REQUIRE(pass);
}
TEST_CASE("Barycentric coordinates: Edge cases") {
int x0 = 0, y0 = 0, x1 = 0, y1 = 10, x2 = 10, y2 = 0;
float b1, b2, b3;
// point on vertex
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 0);
REQUIRE(b1 == 1);
REQUIRE(b2 == 0);
REQUIRE(b3 == 0);
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 10);
REQUIRE(b1 == 0);
REQUIRE(b2 == 1);
REQUIRE(b3 == 0);
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 10, 0);
REQUIRE(b1 == 0);
REQUIRE(b2 == 0);
REQUIRE(b3 == 1);
// point on edge
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 0, 5);
REQUIRE(b1 == 0.5);
REQUIRE(b2 == 0.5);
REQUIRE(b3 == 0);
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 5, 0);
REQUIRE(b1 == 0.5);
REQUIRE(b2 == 0);
REQUIRE(b3 == 0.5);
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, 5, 5);
REQUIRE(b1 == 0);
REQUIRE(b2 == 0.5);
REQUIRE(b3 == 0.5);
}
TEST_CASE("Barycentric coordinates (prop: Σ = 1)") {
int x0 = GENERATE(take(2, random(-100, 100)));
int y0 = GENERATE(take(2, random(-100, 100)));
int x1 = GENERATE(take(2, random(-100, 100)));
int y1 = GENERATE(take(2, random(-100, 100)));
int x2 = GENERATE(take(2, random(-100, 100)));
int y2 = GENERATE(take(2, random(-100, 100)));
int x = GENERATE(take(5, random(-100, 100)));
int y = GENERATE(take(5, random(-100, 100)));
float b1, b2, b3;
std::tie(b1, b2, b3) = barycentric_coordinates(x0, y0, x1, y1, x2, y2, x, y);
REQUIRE_THAT(b1 + b2 + b3, WithinRel(1.0, 1e-4));
}

20
u02/src/util.cpp
View file

@ -139,3 +139,23 @@ Transformation transformation_to_standard_case(int x0, int y0, int x1, int y1) {
return transformation;
}
std::tuple<float, float, float> barycentric_coordinates(int x0, int y0, int x1,
int y1, int x2, int y2,
int xp, int yp) {
// Source:
// https://en.wikipedia.org/wiki/Barycentric_coordinate_system#Vertex_approach
float b1 = x1 * y2 - x2 * y1 + xp * (y1 - y2) + yp * (x2 - x1);
float b2 = x2 * y0 - x0 * y2 + xp * (y2 - y0) + yp * (x0 - x2);
float b3 = x0 * y1 - x1 * y0 + xp * (y0 - y1) + yp * (x1 - x0);
// reciprocal computed directly for performance
float area_factor =
1 / static_cast<float>(x0 * (y1 - y2) + x1 * (y2 - y0) + x2 * (y0 - y1));
b1 *= area_factor;
b2 *= area_factor;
b3 *= area_factor;
return {b1, b2, b3};
}