Question

We are given the triangle with vertices P₁=(1,2),P₂=(4,2),P₃=(1,6). We are also given (r,g,b) colors (in the range 0:255) at the three vertices C₁=(200,200,0),C₂=(0,50,200),C₃=(200,50,100). What is the color at a point inside the triangle Q=(2,3)?

Answer 1

To find the color at a point inside the triangle, we can use barycentric coordinates. The color at a point inside the triangle is a weighted sum of the colors at the vertices using the barycentric coordinates. The barycentric coordinates represent a point inside a triangle as a weighted sum of the triangle's vertices.

Step-by-step explanation:

To find the color at a point inside the triangle, we can use barycentric coordinates. Barycentric coordinates represent a point inside a triangle as a weighted sum of the triangle's vertices. The weights are determined by the relative areas of the sub-triangles formed by the point and the triangle's vertices.

1. Calculate the area of the main triangle using the formula: A = 1/2 * (x1(y2-y3) + x2(y3-y1) + x3(y1-y2))
2. Calculate the barycentric coordinates of the point Q using the formula: alpha = (1/2 * (x2(y3-y) + x(y-x3) + x3(y-y2))) / A, beta = (1/2 * (x(y1-y3) + x1(y-y3) + x3(y1-y)))) / A, gamma = 1 - alpha - beta
3. The color at point Q can be obtained by taking a weighted sum of the colors at the vertices using the barycentric coordinates: R = alpha * R1 + beta * R2 + gamma * R3, G = alpha * G1 + beta * G2 + gamma * G3, B = alpha * B1 + beta * B2 + gamma * B3