In omnidirectional videos, a straight line in the rendering space may no longer appear as a straight line in the frame to be encoded, due to the projection between the encoding space and the rendering space. To adapt to the geometry of omnidirectional videos, intra prediction is performed along non-straight curves. In particular, references samples in neighboring reconstructed blocks of a current block are copied along non-straight curves to form a predicted block for the current block. The non-straight curves may be computed online based on a single intra prediction directional mode for the current block. The parameters of non-straight curves may be based on the mapping used in forming the omnidirectional videos, and the location/size of the current block. The non-straight curves may be obtained using a look-up table or an analytical function that is dependent on the location and size of the current block.