Topologically consistent leafy tree morphing

Abstract

We present a novel morphing technique to generate pleasing visual effects between 2 topologically varying trees while preserving the topological consistency and botanical meanings of any in-between shapes as natural trees. Specifically, we first efficiently convert leafy trees into botanically inspired chain-lobe representations in an automatic way. With the aid of branching-pattern aware, one-to-many correspondences between branches and leaves, we hierarchically interpolate branches of in-between trees while maintaining their topological consistencies. Finally, we simultaneously interpolate foliage, specifically every single leaf, during the morphing process, avoiding the generation of unpleasant "floating" leaves. We demonstrate the effectiveness of our approach by creating visually compelling tree morphing animations, even between cross-species.

Sketch‐based shape‐preserving tree animations

“…Topology‐aware tree animations . Recent works have created topologically consistent animations between two topologically varying trees. However, the work of Wang et al does not handle the animations of foliage.…”

“…However, the work of Wang et al does not handle the animations of foliage. Although the work of Wang et al addresses the smooth transformations of foliage, it fails to preserve the morphological meanings of in‐between trees' crowns, leading to less compelling visual effects when transforming between trees with custom crowns. In addition, this method requires exactly two trees as input, whereas ours only requires one tree and a designer's sketch describing the silhouette of the desired crown.…”

“…Figure illustrates the main steps of our shape‐preserving tree animation approach. Given a leafy tree (Figure a), it is first converted into a branching‐pattern‐aware skeleton‐lobe representation using topologically consistent morphing (Figure b). From a certain viewpoint, designers are allowed to change the shape of the tree by either oversketching the detected crown's silhouette (open sketch) or drawing a new shape describing the desired crown shape under the viewpoint (closed sketch); see Figure c, where the crown silhouettes are plotted in blue, whereas the designers' sketches are plotted in red).…”

“…Other than animating real‐world scenarios, such as the trees' growth process and their interactions with the environment, special requirements in animating stylized trees arise in the film and animation industry in order to nurture the mysterious atmosphere with compelling visual effects . Consequently, topology‐aware approaches have been proposed to generate smooth transformations between trees, achieving visually compelling special effects . However, they do not put explicit efforts into preserving a sequence of morphologically continuous crowns when transforming between trees with specialized crown shapes, leading to less meaningful in‐between trees (see Figure 9, top row).…”

“…To tackle the challenge, we propose a self‐adaptive multiscale cage‐based deformation strategy to hierarchically propagate the transformations of crowns to tree branches. Specifically, the input leafy tree is first abstracted into a skeleton‐lobe representation, where the foliage is clustered into canonical geometries (i.e., lobes ) in order to describe the tree in a hierarchical multiscale manner. The morphologically meaningful and continuous in‐between trees are achieved by first gradually deforming the tree's crown according to the designer's sketch and then hierarchically propagating the deformation to tree branches based on the self‐adaptive multiscale cage tree (MCT), in which the nodes are the view‐dependent silhouettes serving as cages and the edges maintain their topological hierarchies.…”