As we can see the middle picture, the texture was attempted to squeeze the square into a trapezoid via linear transformation in a two dimensional space. In a sense that the lower left triangle and the upper right of the middle image is bound by different transformation matrix. But as the later slide mentioned, the scaling of the texture is not linear, which the projection looks off.
henrykhaung
The way I understand is this. Perspective projection is a way to simulate the way objects appear smaller as they move farther away from the viewer. This creates a nonlinear relationship between the positions of objects in 3D space, which are world coordinates, and their positions on the 2D screen, which are screen coordinates. Because of this, you do not want to apply barycentric interpolation directly in screen space since it assumes a linear relationship between the interpolated values and creates the image we see in the middle. Therefore, we have to instead do interpolation in world space to get the correct image.
antony-zhao
It's a bit interesting to see the wrong projection, especially with the chessboard, to see what happens to various points on the plane. I agree with the previous comments about how it works and what's causing the issues with the projection.
Rogeryu1234
Perspective projection and interpolation are crucial techniques in computer graphics, enabling the creation of realistic 3D scenes. Perspective projection transforms 3D points onto a 2D plane, mimicking how objects appear smaller as they recede into the distance. Interpolation fills in the gaps between known values, ensuring smooth transitions in rendered images or animations. Together, they form the foundation for generating immersive visual experiences in digital environments.
As we can see the middle picture, the texture was attempted to squeeze the square into a trapezoid via linear transformation in a two dimensional space. In a sense that the lower left triangle and the upper right of the middle image is bound by different transformation matrix. But as the later slide mentioned, the scaling of the texture is not linear, which the projection looks off.
The way I understand is this. Perspective projection is a way to simulate the way objects appear smaller as they move farther away from the viewer. This creates a nonlinear relationship between the positions of objects in 3D space, which are world coordinates, and their positions on the 2D screen, which are screen coordinates. Because of this, you do not want to apply barycentric interpolation directly in screen space since it assumes a linear relationship between the interpolated values and creates the image we see in the middle. Therefore, we have to instead do interpolation in world space to get the correct image.
It's a bit interesting to see the wrong projection, especially with the chessboard, to see what happens to various points on the plane. I agree with the previous comments about how it works and what's causing the issues with the projection.
Perspective projection and interpolation are crucial techniques in computer graphics, enabling the creation of realistic 3D scenes. Perspective projection transforms 3D points onto a 2D plane, mimicking how objects appear smaller as they recede into the distance. Interpolation fills in the gaps between known values, ensuring smooth transitions in rendered images or animations. Together, they form the foundation for generating immersive visual experiences in digital environments.