Shader Story

Common HLSL Functions: Cross

cross(a, b) returns a vector that is perpendicular to both input vectors a and b, oriented according to the right-hand rule. Note that the order of inputs matters. cross(a, b) is not the same as cross(b, a), as demonstrated in the visual demo.

It’s essential for calculating surface tangents, bitangents, normal maps, and various geometric operations in shaders.

float3 c = cross(vecA, vecB); // perpendicular to vecA and vecB

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Visual demo

This shader demonstrates the cross() function by computing the perpendicular vector between the surface normal (in view space) and a tangent vector (assumed in tangent space as (1, 0, 0)). The resulting vector is visualized as color output, showing how cross products produce orthogonal directions.

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URP Shader Code

Shader "DecompiledArt/CommonFunctions/Cross/Cross"
{
    Properties
    {
        [Toggle(CROSS_BXA)]_Cross_BxA("Cross_BxA", int) = 0
    }

    SubShader
    {
        Tags { "RenderType" = "Opaque" "RenderPipeline" = "UniversalPipeline" }

        Pass
        {
            HLSLPROGRAM
            #pragma vertex vert
            #pragma fragment frag

            #pragma shader_feature_local CROSS_BXA

            #include "Packages/com.unity.render-pipelines.universal/ShaderLibrary/Core.hlsl"

            struct Attributes
            {
                float4 positionOS : POSITION;
                half3 normalOS   : NORMAL;
            };

            struct Varyings
            {
                float4 positionHCS : SV_POSITION;
                half3 normalVS    : TEXCOORD0;
                half3 tangentTS   : TEXCOORD1;
            };

            Varyings vert(Attributes IN)
            {
                Varyings OUT;

                half3 normalWS = TransformObjectToWorldNormal(IN.normalOS);

                OUT.normalVS = mul((float3x3)UNITY_MATRIX_V, normalWS);
                OUT.tangentTS = half3(1, 0, 0); // In tangent space, the tangent vector is always (1,0,0)

                OUT.positionHCS = TransformObjectToHClip(IN.positionOS.xyz);
                return OUT;
            }

            half4 frag(Varyings IN) : SV_Target
            {
                #ifdef CROSS_BXA
                    half3 col_output = cross(IN.tangentTS, IN.normalVS);
                #else
                    half3 col_output = cross(IN.normalVS, IN.tangentTS);
                #endif

                return half4(col_output, 1.0);
            }

            ENDHLSL
        }
    }
}

URP Shader graph

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🔗 Related Functions

Dot

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