A dynamic chart where the user can apply filters on the categorical variables.
I would also like the related database to remain inaccessible to the user.
An example of such chart.
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The Shiny app by the folks from RStudio helps you do that. It is a web application framework for your R analytics and code.
It helps you apply requisite filters which you can define, and you can decide on including the database access permissions too.
Similar to what Dawny mentioned above, there is also Plot.ly which you can use exactly like you would use Excel online. There is also a Powerpoint add-on to have the interactive graphs inside powerpoint presentations. Just in case you don't know, or don't want to learn
R (though you should, because Shiny is awesome).
And for the sake of completeness, the graph that you linked above was created using Google Charts, which you can use from
R and share on ShinyApps through RStudio really easily. The package is called GoogleVis.
You can program any filtering routine you want, but you will probably have to do the implementation yourself. At least, I'm not aware of a connection between flotplot and an extensive math library like R.
Flotplot only sends the user the data needed to plot the curves, so users won't be able to access the whole database at once.
You can try Web Pivot Table. It is totally web based and run inside browsers and it has full functionalities as excel pivot table.
It creates pivot table and pivot chart synchronizedly and support OLAP cube pivot as well.
It has two editions. Free edition is free for anyone or any company. Professional edition can be embedded into any other applications or software and need to purchase a license.