What is a vertice - how does it separate from a triangle?
Can vertices be shared?
In what do you define a vertice? What else?
The points that enable the definition of a mesh/triangle
Vertices can be shared
In 3d space but as well e.g. texture and color
How does 2d transformation work? Give an example
Why do we chose matrix transformation instead of vectors? What is important to be kept in mind?
From which side are the multiplications applied first?
How can a matrix be decomposed into rotation x scale x rotation?
Vector multiplication follows just simply the concept of changing coefficients in what we multiply with.
E.g. for shear:
Because we can save on opertations to carry out which on scale of many vertices saves a huge am ount of resources. This is done by applying the product of two matrices instead of two tranformation on eahc. (matrix multiplication is assiciative)
The order of eecution is important as this can have different impact on the outcome
From the right side
Via Singular value decomposition
What is special about translation compared to e.g. scaling?
How can this be over come?
What is rigid body transforms?
What does change for translations in 3d?
With 2x2 the translations are not applicable which is linear wherefore we can’t “shift” our objects away from the origin
With 3x3 matrices employing a homogenous coordinate (the 1)
rigid body: only contains rotations and translations
For 3d we need a 4x4 matrix to contain the homogenous coordinate
Explain viewport transformation
What are normal vectors? What is the ‘issue’?
How can we solve this?
Properties of vertices, they describe directions and not positions
They can’t be transformed with our model due to not staying perpendicular
By focusing on the perpendicular attribute and the dot product being 0. M is for position vectors, N is for direction vectors
How would you handle transformation position and direction vectors respectively
For directions vector we sometimes need as well direction vector
How can you calculate the inverse transformation?
M1 would be mutiplied with M1^-1
What are projections used for and what types do we have? Which type is used in computer graphics?
Projection is to map 3d models into the 2d screen space so making pixels out of vertices and triangles
Orthographic projection - what is parallel stays parallel
Perspective projection - pov as camera our human, vanishing ponts
Explain the orthograhic prpojection
How can we map the camera coordinate system (e) to the world coordinate system (o)
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