iPad PDF reader app with seamless handwritting annotation experience I am looking for an iPad app (Android app references will also be considered useful) which allows reading PDF files and annotating them with a stylus, resembling the experience I would have with a pen and a piece of paper as closely as possible.

This requires:


Not enforcing to go through button clicking, context menus or popups
every time I want to write something. (i.e. add annotation, accept
annotation). It completely breaks the reading experience.

I don't even care if that kind of a step-based work-flow is better if you want to edit/delete the annotations. I would be happy even if deletion/edition was not allowed, a good old cross-out would be enough for me.
The writing experience should be snappy and responsive. I don't want lines to follow my stylus-tip as I write, like laggy comets in orbit. A good example of good behaviour in this regard is Wacom's Bamboo Write App


Optionally it would be simply awesome if it was had handwritting calculator capabilities like MyScript Calculator. I am used to make calculations in the margins, when reading engineering or math-related books.

I have tried Goodreader and iAnnotate but neither of them comply with (1) or (2). Any suggestions?
I found it! Good notes does exactly (1) and (2) 

You can write without accessing menus and browse the document at the same time by using two-finger gestures (to distinguish them from the writing itself). And writing is really snappy.

It also happens to have a great feedback system, so I added a suggestion to add a handwritting calculator.

The only missing features (for my taste) are margin cropping and automatic Dropbox synching.