Modeling and Rendering of Metallic Patinas

Julie Dorsey, Pat Hanrahan

Ionel Daniel Stroe
CS 563

Feb 10th, 1999 


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More and more powerful techniques have been developed lately for generation of synthesis images. More and more technology has been directed towards creating of complex realistic effects. However, a common criticism of such images is that they look too ideal. Here originates the need of creating a new and natural look for these synthesis images. Some of these efforts have been focused on modeling weathering effects. Weathering generic defines any change in appearance , deterioration or decay determined by the surrounding environment. Specific examples of weathering include the corrosion of metals, efflorescence on stone and brick, fungal attack on organic materials, and the wear and tear of everyday life [1].

The present paper addresses the problem of modeling and rendering of metallic patinas. A patina is a film or incrustation on a metallic surface produced by a chemical alteration of the surface, usually associated with removal or addition of material. The method is important not only for its application in computer graphics but also in other related fields, such as urban architecture (future appearance of buildings can be predicted), archeology (past appearance of an object can be generated), etc.

Physical Basis
The metal used as a case study during the entire paper is copper. The patinas of copper and copper alloys are classical examples of layered structures. When viewed in cross section, multiple layers are distinctly visible to the eye. 

When exposed to the atmosphere, a clean copper surface quickly forms a thin layer of brown tarnish that gradually changes with time to a reddish brown color. This color is an indicative of mineral cuprite (copper oxide). Once this layer is in place, subsequent layers grow much more slowly. However, in time, other layers are formed on the top of this. First, a dark brown layer of copper sulphides is developed and then organic copper salts such as nitrates or sulphides which give the aged copper its specific green color are formed.

The formation of real patina dramatically depends on the natural environment. The same layers are formed, but their thickness and distribution depends on the length of exposure and chemical characteristics of the medium which change from one environment to another. The figure below depict the process of formation metallic patinas in three different environments: marine, rural, and urban.


As shown in previous section the metallic patinas has a natural representation as a stack of layers. Moreover, there is not an overall profile for such a process because of its dependence on the surrounding environment. Therefore, the process will be modeled as set of layers on which some operators can be applied. The parameters of these operators as well as the succession in which they are applied depends exclusively on the application (/ designer options).

Each layer is modeled as a 2D array and further mapped as a texture on the desired object. There could be n such layers, of different thickness, potentially with different physical properties. The thickness may vary as a function of spatial position or may not. The physical properties are expressed using two rendering parameters: transmittance and reflectance. Basically, the first layer has a zero transmittance (it is assumed to be infinite).

The process of aging is simulated by applying a set of operators on these layers. The operators are presented below:

  • coat (material, thickness, thickness-map)

  • apply a given thickness layer of material on a given thickness-map
  • erode (thickness, thickness-map)

  • remove a given thickness of material from the thickness map
  • fill (material, height, thickness-map)

  • add material on a thickness map until a given height is reached
  • polish (material, height, thickness-map)

  • remove all the material from a thickness map
    that is higher that a given height

Thickness Map

In order to simulate the variation of thickness over time some fractal surface growth models have been implemented. The models describe the deposit of materials over time as well as the growth of the patches on surfaces. Moreover, various growth rates were also considered (such as linear, parabolic, logarithmic).
  • random deposition (RD)

  • From randomly chosen position on the texture map (thickness map), a particle falls vertically until it reaches the top of the surface, whereupon it is deposited.

  • ballistic deposition (BD)

  • BD is similar to RD; only that a particle may also stick laterally, allowing the patch to grow in size (area).

  • direct percolation depinning (DPD)

  • An addition 2D vector for marking whether a cell is blocked or not is used. First, a percentage of cells are marked as blocked or not. Then, a random model of expansion is used in order to simulate the growth of the patch.

    The figure depicts the growth of two patches when different percentage of initially blocked cells were used.

Rendering Metallic Patinas

The stack of layers (with transmittance and reflectance coefficients for each layer) can be rendered using the Kubelka-Munk model described in [2]. This is basically a one-dimensional volume radiosity which, in addition, several layers are combined. The resulting coefficients obtained when combining two layers are given by the following formulas (R-reflectance, T-transmittance):

Experimental Results

Copper Strips. The method was first tested on copper strips. A marine, an urban, and rural environment were simulated. The process and the result are presented below:

Statue of Buddha. Second, the method was applied on a copper statue. In this example, information about the wetness and the accessibility (geometrical position of the points) was used during simulation. A movie (141k) for this experiment is available (click the image below).

Towers. Finally, metallic roofs in a urban environment were used to show the aging process in different stages. A noise function was added here to simulate the dirt from the atmosphere.


[1]    Dorsey, J.; Hanrahan, P.: "Modelling and Rendering of Metallic Patinas", SIGGRAPH, Aug 1996
[2]    Kortum, G.: "Reflectance Radioscopy", Springer-Verlag, New York, 1969


Some of the figures used in this presentation have been obtained from [1].
The movie has been dowloaded from