A computer-implemented method for rendering an image of hair in a computer-generated scene, the method comprising: accessing the computer-generated scene, the computer-generated scene comprising at least one virtual light source and at least one virtual object, wherein the virtual object represents at least a portion of one or more hairs and the virtual object comprises a geometry model and a material model, the geometry model defining a shape of the virtual object and the material model defining how light reflects, transmits, and scatters as it intersects the virtual object; accessing a virtual camera, the virtual camera having a position and a direction through which the computer-generated scene is viewed; accessing a hair shading function, wherein the material property model of the virtual object is defined at least in part by the hair shading function; wherein the hair shading function comprises at least one specular lobe component, the at least one specular lobe component based on a width value and an offset value, and wherein the width value represents a roughness of the virtual object and the offset value represents a shift of the reflective highlight of the virtual object; generating a set of random values; importance sampling the hair shading function by converting the set of random values into a set of light direction samples, each light direction sample of the set of light direction samples having a probability density function that is proportional to the value of the hair shading function at the light direction sample; wherein converting the set of random values into the set of light direction samples is based on a Cauchy distribution, and the probability density function of each converted light direction sample uses a Cauchy distribution; computing a light color value for each light direction sample of the set of light direction samples; computing a hair color value using the hair shading function for each light direction sample of the set of light direction samples; weighting the light color value and the hair color value computed for each light direction sample to determine a set of weighted values, wherein the weighting uses the corresponding probability density function of each light direction sample; determining a characteristic of a pixel, wherein the pixel represents part of the virtual object within the image as viewed through the virtual camera; and wherein the characteristic of the pixel is based on the set of weighted values. accessing the computer-generated scene, the computer-generated scene comprising at least one virtual light source and at least one virtual object, wherein the virtual object represents at least a portion of one or more hairs and the virtual object comprises a geometry model and a material model, the geometry model defining a shape of the virtual object and the material model defining how light reflects, transmits, and scatters as it intersects the virtual object; accessing a virtual camera, the virtual camera having a position and a direction through which the computer-generated scene is viewed; accessing a hair shading function, wherein the material property model of the virtual object is defined at least in part by the hair shading function; wherein the hair shading function comprises at least one specular lobe component, the at least one specular lobe component based on a width value and an offset value, and wherein the width value represents a roughness of the virtual object and the offset value represents a shift of the reflective highlight of the virtual object; generating a set of random values; importance sampling the hair shading function by converting the set of random values into a set of light direction samples, each light direction sample of the set of light direction samples having a probability density function that is proportional to the value of the hair shading function at the light direction sample; wherein converting the set of random values into the set of light direction samples is based on a Cauchy distribution, and the probability density function of each converted light direction sample uses a Cauchy distribution; computing a light color value for each light direction sample of the set of light direction samples; computing a hair color value using the hair shading function for each light direction sample of the set of light direction samples; weighting the light color value and the hair color value computed for each light direction sample to determine a set of weighted values, wherein the weighting uses the corresponding probability density function of each light direction sample; determining a characteristic of a pixel, wherein the pixel represents part of the virtual object within the image as viewed through the virtual camera; and wherein the characteristic of the pixel is based on the set of weighted values.