represent a point within a triangle using the weighted sum of its vertices. Alpha, beta and gamma are weights
also, represent the distance from a point to the triangle's vertices
saif-m17
I'm a bit confused on what the triangle itself represents when V_A, V_B, V_C are colors. I understand that the points within the triangle are some combination of those colors (like RGB values maybe), but I'm not entirely clear what the physical/geometric interpretation of the coordinate system is.
sgk12
I might be off here, but to my understanding the triangle itself doesn't factor into the given formula — when V_A, V_B, and V_C are colors and alpha, beta, and gamma intuitively represent "how intense" each color is when combined into the final value. I'm visualizing it as mixing colors on a palette — alpha determines how much red, beta determines how much green, and so on. In this specific case, I don't think the equation necessarily refers to a physical coordinate system — it's merely a combination of colors (expressed as numerical values, I assume).
jerrymby
If VA VB VC encode information about the surface orientation such as little dents, then linear combination of orientation vectors assumes the surface to be flat. Would this cause problems when the surface have curvatures?
0-0-00-0
@saif-m17 For example, the coordinate value α is basically how far away you are from the edge BC compared to the distance from the vertex A to BC.The closer you are to BC, the farther you are from A and the less share of weight you get from A's color. Another interpretation (as shown in a few slides later) could be the ratio of the area of △VVBVC to the area of △VAVBVC. This one is cleaner in showing that the coordinate values sum up to 1.
jjaison
I'm a bit confused as to what we're interpolating in the case with texture maps. the color example makes sense because interpolation could be interpreted as mixing together to get intermediate color values, but in the context of texture maps, what are we interpolating over?
0-0-00-0
@jerrymby The surface curves themselves should be represented by distributions of little flat triangles. This one is coloring just a single one of such triangle (not 100% sure though)
Rogeryu1234
Linear interpolation across a triangle using barycentric coordinates is a powerful technique in computer graphics for smoothly blending values between vertices. By expressing a point within a triangle as a combination of its vertices' weights (barycentric coordinates), interpolation becomes straightforward. This method ensures geometric correctness and is widely used in rendering algorithms like rasterization and ray tracing, enabling realistic shading and texture mapping effects.
OnceLim
It's interesting to see how something we learned early on in the semester is still very prominently used in our final project. Not just linear interpolation across triangles, but interpolation in general seems very important throughout graphics.
I'm a bit confused on what the triangle itself represents when V_A, V_B, V_C are colors. I understand that the points within the triangle are some combination of those colors (like RGB values maybe), but I'm not entirely clear what the physical/geometric interpretation of the coordinate system is.
I might be off here, but to my understanding the triangle itself doesn't factor into the given formula — when V_A, V_B, and V_C are colors and alpha, beta, and gamma intuitively represent "how intense" each color is when combined into the final value. I'm visualizing it as mixing colors on a palette — alpha determines how much red, beta determines how much green, and so on. In this specific case, I don't think the equation necessarily refers to a physical coordinate system — it's merely a combination of colors (expressed as numerical values, I assume).
If VA VB VC encode information about the surface orientation such as little dents, then linear combination of orientation vectors assumes the surface to be flat. Would this cause problems when the surface have curvatures?
@saif-m17 For example, the coordinate value α is basically how far away you are from the edge BC compared to the distance from the vertex A to BC.The closer you are to BC, the farther you are from A and the less share of weight you get from A's color. Another interpretation (as shown in a few slides later) could be the ratio of the area of △VVBVC to the area of △VAVBVC. This one is cleaner in showing that the coordinate values sum up to 1.
I'm a bit confused as to what we're interpolating in the case with texture maps. the color example makes sense because interpolation could be interpreted as mixing together to get intermediate color values, but in the context of texture maps, what are we interpolating over?
@jerrymby The surface curves themselves should be represented by distributions of little flat triangles. This one is coloring just a single one of such triangle (not 100% sure though)
Linear interpolation across a triangle using barycentric coordinates is a powerful technique in computer graphics for smoothly blending values between vertices. By expressing a point within a triangle as a combination of its vertices' weights (barycentric coordinates), interpolation becomes straightforward. This method ensures geometric correctness and is widely used in rendering algorithms like rasterization and ray tracing, enabling realistic shading and texture mapping effects.
It's interesting to see how something we learned early on in the semester is still very prominently used in our final project. Not just linear interpolation across triangles, but interpolation in general seems very important throughout graphics.