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Strokes painted in the 2D viewport window must be embedded in 3D space in a way that gives creative freedom to the artist while maintaining an acceptable level of controllability. We address this challenge by proposing a canvas concept defined implicitly by a 3D scalar field. The artist shapes the implicit canvas by creating approximate 3D proxy geometry. An optimization procedure is then used to embed painted strokes in space by satisfying different objective criteria defined on the scalar field. This functionality allows us to implement tools for painting along level set surfaces or across different level sets. Our method gives the power of fine-tuning the implicit canvas to the artist using a unified painting\/sculpting metaphor. A sculpting tool can be used to paint into the implicit canvas. Rather than adding color, this tool creates a local change in the scalar field that results in outward or inward protrusions along the field's gradient direction. 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