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Given two disks D1 and D2. Their radii, positions, and velocities are known. How can I predict whether they will collide or not? For a head-on collision, the angles that the directions of motion make with the x-axis add up to 180 degrees. But I don't know what is the condition for an oblique collision. Any help would be appreciated.

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Given the velocities and positions, first consider the two bodies to be point objects and find the distance of closest approach between the two points (centers). If this distance ($d_c$) is zero, then they collide head-on, if $d_c <r_1+r_2$, then they will collide, or else they won't collide.

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