Barycentric coordinates - Revision history

Vegard: add link

2020-02-17T15:51:52Z

add link

← Older revision		Revision as of 15:51, 17 February 2020
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	}		}
	</source>		</source>

			=== See also ===

			* https://asawicki.info/news_1721_how_to_correctly_interpolate_vertex_attributes_on_a_parallelogram_using_modern_gpus

	[[Category:Graphics programming]]		[[Category:Graphics programming]]

Vegard at 21:35, 31 December 2019

2019-12-31T21:35:30Z

← Older revision		Revision as of 21:35, 31 December 2019
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			Barycentric coordinates let you represent a coordinate as a weighted sum of three points. This can be very useful for interpolating values across a triangle, including world coordinates or texture coordinates.

	=== Conversion from cartesian ===		=== Conversion from cartesian ===

Vegard: use glm

2019-12-29T13:43:23Z

use glm

← Older revision		Revision as of 13:43, 29 December 2019
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	// Compute barycentric coordinates (u, v, w) for		// Compute barycentric coordinates (u, v, w) for
	// point p with respect to triangle (a, b, c)		// point p with respect to triangle (a, b, c)
			glm::vec3 barycentric(glm::vec3 a, glm::vec3 b, glm::vec3 c, glm::vec3 p)
	void Barycentric(Point p, Point a, Point b, Point c, float &u, float &v, float &w)
	{		{
	~~Vector~~ v0 = b - ~~a, v1~~ = ~~c - a, v2 = p~~ - a;		auto v0 = b - a;
	~~float~~ ~~d00~~ = ~~Dot(v0,~~ ~~v0)~~;		auto v1 = c - a;
	~~float~~ ~~d01~~ = ~~Dot(v0,~~ ~~v1)~~;		auto v2 = p - a;

⚫	float ~~d11~~ = ~~Dot(v1,~~ ~~v1)~~;
	float ~~d20~~ = ~~Dot~~(v2, v0);		float d00 = glm::dot(v0, v0);
	float ~~d21~~ = ~~Dot~~(v2, v1);		float d01 = glm::dot(v0, v1);
	~~float~~ ~~denom~~ = ~~d00~~ * d11 ~~- d01~~ * ~~d01~~;		float d11 = glm::dot(v1, v1);
	v = ~~(d11~~ * d20 - ~~d01~~ * d21) ~~/ denom~~;		float d20 = glm::dot(v2, v0);
	w = ~~(d00~~ * d21 - ~~d01~~ * d20) ~~/ denom~~;		float d21 = glm::dot(v2, v1);
	u = ~~1.0f~~ - v - w;		float denom = d00 * d11 - d01 * d01;

			float v = (d11 * d20 - d01 * d21) / denom;
			float w = (d00 * d21 - d01 * d20) / denom;
		⚫	float u = 1.0f - v - w;

			return glm::vec3(u, v, w);
	}		}
	</source>		</source>
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	<source lang="C++">		<source lang="C++">
	// https://stackoverflow.com/a/11262425		// https://stackoverflow.com/a/11262425
			glm::vec3 cartesian(glm::vec3 a, glm::vec3 b, glm::vec3 c, glm::vec3 p)
	Vector3d Tri::cartesian(const Vector3d& barycentric) const
	{		{
	return ~~barycentric.x~~ * p0 + ~~barycentric.y~~ * p1 + ~~barycentric.z~~ * p2;		return a * p.x + b * p.y + c * p.z;
	}		}
	</source>		</source>

Vegard at 13:36, 29 December 2019

2019-12-29T13:36:01Z

@@ Line 17: / Line 17: @@
     w = (d00 * d21 - d01 * d20) / denom;
     u = 1.0f - v - w;
+}
 </source>

Vegard: new page

2019-12-29T13:34:14Z

new page

New page

=== Conversion from cartesian ===

<source lang="C++">
// https://gamedev.stackexchange.com/a/23745
// Compute barycentric coordinates (u, v, w) for
// point p with respect to triangle (a, b, c)
void Barycentric(Point p, Point a, Point b, Point c, float &u, float &v, float &w)
{
Vector v0 = b - a, v1 = c - a, v2 = p - a;
float d00 = Dot(v0, v0);
float d01 = Dot(v0, v1);
float d11 = Dot(v1, v1);
float d20 = Dot(v2, v0);
float d21 = Dot(v2, v1);
float denom = d00 * d11 - d01 * d01;
v = (d11 * d20 - d01 * d21) / denom;
w = (d00 * d21 - d01 * d20) / denom;
u = 1.0f - v - w;
}
</source>

[[Category:Graphics programming]]
[[Category:Geometry]]