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Specify parallel camera position in world. Right now its position is [0, 0, -1] which is the same as that of perspective camera with fixed eye position. However, parallel camera now renders and picks even nodes behind camera. If we just fix the near/far clip planes for it, it stops to render anything above Z=-1. Consider moving the fixedEyePosition to Camera, although I'm not sure how to define the non-fixed position for parallel camera as there is no field of view. Perhaps it could have a double zPosition property, by default set somewhere farther than -1. Feel free to assign to me for coding when the specification is cleared.
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